
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
Given a triangle with sides of lengths 3, 4, and 5. Three circles are constructed with radii of 1, centered at each vertex of the triangle. Find the total area of the portions of the circles that lie within the triangle.

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