Formal:
* Deliberation: implies a serious and thoughtful consideration of options.
* Contemplation: suggests a deep and sustained thinking about a particular subject.
* Cogitation: indicates a slow and careful mental process.
* Meditation: refers to focused concentration and reflection.
* Reflection: involves thinking carefully about past experiences or ideas.
* Analysis: a detailed examination of something, often to understand its parts.
Informal:
* Thinking things through: implies careful consideration of all aspects of a situation.
* Weighing your options: suggests carefully considering the pros and cons of different choices.
* Mulling it over: implies slow and thoughtful consideration.
* Giving it some thought: a general expression for considering something carefully.
Other options:
* Discernment: implies a careful and insightful understanding.
* Judgment: suggests a considered opinion or decision.
* Reasoning: the process of thinking logically and systematically.
The best word for you will depend on the specific context of your writing.