
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 the isosceles triangle \( M N K \), the sides \( M N = N K = 12 \) and \( M K = 8 \). A point \( F \) is chosen on the side \( N K \) such that the incircles of triangles \( M N F \) and \( M K F \) touch each other. Find the areas of triangles \( M N F \) and \( M K F \).

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