
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
A circle is inscribed in a triangle  $ABC$  with sides  $a,b,c$ . Tangents to the circle parallel to the sides of the triangle are contructe. Each of these tangents cuts off a triagnle from  $\triangle ABC$ . In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of  $a,b,c$ ).

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