
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 median \( CM \) is drawn from the right angle \( C \) of the triangle \( ABC \). A circle inscribed in the triangle \( ACM \) touches the side \( CM \) at its midpoint. Find the angles of triangle \( ABC \).

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