
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 such that:

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

How many degrees is the angle \(\angle BAM\)?

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