
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 $A B C$ where $A B = A C$ and $\angle A B C = 53^{\circ}$. Point $K$ is such that $C$ is the midpoint of segment $A K$. Point $M$ is chosen so that:

- $B$ and $M$ are on the same side of line $A C$;
- $K M = A B$;
- $\angle M A K$ is the largest possible.

How many degrees is the angle $\angle B A M$?

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