Just to give you a look at one specific speech that demonstrates Hamlet's thinking and suggests the possibility that his thinking contributes to his delay, I'll briefly add to the exceptional answer above.
In Hamlet's famous "To be or not to be" speech (Act 3.1.56-87), he ponders the state of existence. To be is to exist. Hamlet wonders if existence, with its "slings and arrows of outrageous fortune," is worth the trouble.
He thinks about the perils of existence compared to the possible perils of the afterlife. He concludes that if one did not have to be afraid of what might come after death, one would be smarter to not exist at all. But, since the afterlife is an "undiscovered country" from which "No traveller returns," it is better to bear the "ills" we know, than to take a chance on those we don't.
The details of his speech present Hamlet's capacity for thinking, but for your purposes you need not even go into the details. What matters in answering your question is that Hamlet is thinking about the general issue of existence here, rather than thinking about the specific issue of his revenge.
If you want to make the argument that Hamlet's thinking gets in the way of his revenge, this speech is a possible piece of evidence. Hamlet can't just seek revenge, one could argue, he must first consider every angle. One could say that Hamlet should be planning revenge, here, not contemplating existence. You may or may not be correct if making this argument, but if this is your assignment this speech may help.