
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
The circumference of a circle is 80 feet. Inside this circle, there are two marked angles at points \( A \) and \( M \) from the center \( O \). Angle \( \angle AOM \) is \( 45^\circ \), and angle \( \angle MOB \) is \( 90^\circ \). Calculate the lengths of \( \widehat{AM} \) and \( \widehat{MB} \).

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