
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 an isosceles triangle \( ABC \), where \( AB = AC \) and \( \angle ABC = 53^\circ \). Point \( K \) is such that \( C \) is the midpoint of segment \( AK \). Point \( M \) is chosen so that:

- \( B \) and \( M \) are on the same side of line \( AC \),
- \( KM = AB \),
- the angle \( \angle MAK \) is as large as possible.

What is the measure of angle \( \angle BAM \) in degrees?

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