
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]


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In triangle \( \triangle ABC \), draw the circle that is tangent to its sides. What are the lengths of the sides and the angles of the triangle if the lengths of the sides of the triangle defined by the points of tangency are \( 25 \text{ cm} \), \( 29 \text{ cm} \), and \( 36 \text{ cm} \)?

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