
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 an isosceles triangle \(MNK\) with sides \(MN = NK = 8\) and \(MK = 4\), a point \(F\) is chosen on side \(NK\) such that the incircles of triangles \(MNF\) and \(MKF\) are tangent to each other. Find the areas of triangles \(MNF\) and \(MKF\).

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