
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 vertices of a triangle are connected to the center of the inscribed circle. The segments thus drawn divide the area of the triangle into three parts, equal to 28, 60, and 80. Find the sides of the triangle.

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