You certainly may use thinking skills to pursue an understanding of your purpose in life--how readily that purpose will become apparent is a different question. Starting with becoming apparent, the reason for this is that understanding ourselves comes, in part, through experience. This is one reason higher education is amazingly valuable to the young person: if pursued fully, it provides experience, opportunity, insight. These are all required fuel for keen, effective thinking skills.
While emotions may be part of finding your purpose in life, it is not true that emotions help all people find their purpose and it is not true that emotions are pure and unsullied by external influences. Since these things are not true, you must rely on your thinking skills even to understand your emotions. Suppose, for example, you have a domineering, unkind family member who relishes telling you unpleasant and false things about yourself. This person embeds thoughts and feelings in you that are equally false. Thus if you look to your emotions, you will find impure emotions that are other-generated and not helpful to you in finding your way to your purpose in life.
Your thinking skills, backed by experience (enough experience to help sort through mistaken other-generated thoughts and emotions), allow you to look at your strengths and weaknesses; allow you look at your interests and limitations; allow you to trust yourself (for instance, if you like science but cannot bear to hear about Hydrogen, "the simplest element," one more time, you will trust yourself to say to your teacher that you would like to hear more complex examples instead of close your mind to science); allow you to see your inner nature and character for what they are. From these things, you can extrapolate what your overall purpose in life is (whether you think it is a choice or something born in you).
Then ... your thinking skills can help you to select how to express this purpose. For example, if your purpose is to teach, you might do it as teacher or a professor or as a clergy-person or as a training manager or as a motivational writer. Your thinking skills are definitely your best resource for discovering your purpose in life.
I think the most simple approach is to use your thinking skills to really analyze and prioritize what is really important to you. Whether it is career, religion, family, or some other thing; once you have a clear understanding of what you value in life, you can have a better sense of what your purpose in life is.
A purpose in life may involve many different considerations; determining that purpose will probably require use of many sources of input.
Thinking skills can be helpful as one analyzes personal interests and abilities. One may use comparison and contrast techniques to evaluate personal priorities and values that shape actions and attitudes. One may need to assess comments and suggestions offered by others, identifying input that matches personal value systems.
Based on the conclusions of such thought processes, a person can identify activities that are important for ones values, reasons for believing as one does, and methods of demonstrating the priorities and purposes one considers to be most important in life.
While everything said in the previous posts is true, there is also a sense in which we cannot possibly use our thinking skills to discover our purpose in life. In many ways, our purpose in life is something that we feel much more on an emotional level than on an intellectual one. We cannot use thought, for example, to determine if we will have faith in God. We cannot use thought to determine that we love our families more than anything else and will devote our lives to them. These are things that we feel emotionally, not intellectually.
It is very easy to go through stretches of our lives without doing any serious thinking about our direction in life. We can tend to just muddle through, dealing with day to day difficulties and challenges, without analyzing what we are doing.
Applying analytical skills to our lives by looking closely at what makes us happy or unhappy, fulfilled or empty, satisfied or longing, can help us direct our lives in a more positive way and help us find that purpose that you're asking about. But you have to be willing to face the truth about yourself. Sometimes that's not easy to do.
By thinking, we can strip away some of our irrational responses and impulses that can easily dominate our daily lives. Thinking is different from just reacting, it takes more effort and introspection.
A person can use their thinking skills to find their purpose in life by performing an analysis of their past behavior, their current situation, and the goals they desire to achieve in the future. Their thinking skills can be put to use pondering how the thoughts, actions, and situations of their past have positioned them where they are today. If they do not like their current station in life, they must analyze the decisions in the past that brought them to where they now are. Then, they can take action to rectify (as much as is possible) their current situation.
In addition, a person can undertake a critical analysis of their present state, and with clear objectives in mind, make decisions that will move them forward to the achieving of these goals. After determining their present situation, they may see that they require more education, mentoring, financial resources, help from family and friends, and such to help them achieve their goals, all designed to give them a better future. Focused thinking will lead to the decisions that lead to the actions that help them find and achieve their purpose in life.
Our purpose in life is something that can be seen from a few different perspectives. There are those who believe that a purpose created by a higher power is "given" to us, while there are those who believe that it is up to us to determine our own purpose. There are also those who believe that our lives are essentially purposeless.
Those in the first category usually find a sense of purpose more through feeling than thinking, but if one wants to find a sense of purpose through a thought process, that would probably involve cataloging one's talents and interests, considering all the possible applications of them, and then choosing a purpose that is in keeping with those.
I agree that we have short-term, intermediate, and long-term purposes in life, and the best way to achieve purposefulness is probably to make sure that one's shorter-term purposes are consistent with our overall purposes.
n some ways, one could say that the discipline of ethics has been struggling with that issue for approximately 2,500 years and so finding a simple and quick answer is highly improbable. Very few people have a singular purpose in life, with the exception for fanatics, saints, and the insane. Most of us have multiple purposes, some short term, such as career objectives, some interpersonal (e.g. parents trying to create a good life for their children), some ethical ideals pertaining to communities (helping the homeless, environmental activism, etc.) and some religious and spiritual. One way you can use critical thinking skills is by measuring short term rewards against long term goals. For example, is going to a party the night before an exam or studying a better choice in the long term? Or, if you have a part-time job, rather than spending all your money on yourself, would you be developing a more ethical character by giving 10% to causes you believe in? or should you be donating a few hours a week of your time to local charities?