What steps did Abraham Lincoln take to avoid war?
I would say that Lincoln's basic strategy for avoiding war was trying not to antagonize the South. He did this through his actions and through his words.
In his inaugural address, Lincoln was very conciliatory. He spoke about how there was no need for bloodshed and he talked about how the North and the South were one country with a common heritage. He also pledged that he would not try to "interfere" with slavery in the places where it was legal at that time.
In terms of his actions, Lincoln was also pretty conciliatory. For example, he did not send reinforcements to Fort Sumter. He thought that that would be too aggressive of an action. Instead, he just tried to send supplies.
So the point is that Lincoln tried to do and say things that would A) keep the Union together and B) avoid making the South too angry. These were the steps he took to try to avoid war.
Even before Lincoln took office of the President in 1861, Seven States in South had seceded and declared themselves a new nation. Lincoln did not accept this position and hoped to reunite the nation.
His attempts at this started right from his inaugural address on March 4, 1861. In his address he expressed his commitment to support the Crown Amendment to the constitution, to protect slavery in states where it already existed. Subsequently he wrote letters to all the governors and sought their support for ratifying this amendment.
To avoid war Lincoln decided not to take any action against the south, unless they attacked first. Lincoln was finally forced to take action against south when on April 12, 1861 army controlled by Southern States fired upon Union troops at Fort Sumter and forced them to surrender.