
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In a triangle with sides \(AB = 4\), \(BC = 2\), and \(AC = 3\), an incircle is inscribed. Find the area of triangle \(AMN\), where \(M\) and \(N\) are the points of tangency of this incircle with sides \(AB\) and \(AC\) respectively.

Present the answer in LaTex format: \boxed{Your answer}
user