
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
Segment $AB$ has midpoint $M$, and segment $MB$ has midpoint $N$. Semi-circles are constructed with diameters $\overline{AB}$, $\overline{MB}$, and $\overline{NB}$ to form the entire region shown. Segment $MP$ splits the region into two sections of equal area. What is the degree measure of angle $AMP$?

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