
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
The incircle is inscribed in a triangle \(ABC\) with sides \(a, b, c\). Three tangents to the incircle are drawn, each of which is parallel to one side of the triangle \(ABC\). These tangents form three smaller triangles (internal to \(\triangle ABC\)) with the sides of \(\triangle ABC\). In each of these triangles an incircle is inscribed. Determine the sum of areas of all four incircles.

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