
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
Let \(a, b, c\) be the lengths of the sides of triangle \(ABC\). Draw the lines tangent to the incircle of triangle \(ABC\) and parallel to its sides. These tangents cut off three smaller triangles from triangle \(ABC\); in each of these smaller triangles, draw the incircle again. Calculate the sum of the areas of the four incircles.

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