
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 triangle \( \triangle ABC \) with side lengths \(a\), \(b\), and \(c\), an inscribed circle is drawn. Construct three tangents from this circle, each parallel to one side of the triangle. These tangents intersect the original triangle to form three new triangles. Construct the inscribed circle in each of these three new triangles. Find the sum of the areas of the four circles formed.

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