If I am acting based on a compulsion, then I am acting because I am forced to do so. I have given up my power to chose. What is the opposite of this? If I decide to act after careful analysis and decision, what is this called?
You can say you're acting "deliberately" or "with careful deliberation".
From the MacMillanDictionary.com:
1) with a definite intention, not by chance or by accident
Examples: "You did that deliberately, just to annoy me.",
"Police believe the fire was started deliberately."
"Her voice was deliberately cool."
2) in a slow careful way
Example: "He spoke deliberately, considering each word carefully."