
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
From the vertex of the right angle of triangle \(ABC\), the median \(CM\) is drawn. The circle inscribed in triangle \(CAM\) touches \(CM\) at its midpoint. Find the angle \(BAC\).

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