
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 axial section $SAB$ of a conical frustum is an equilateral triangle with side length 2. $O$ is the center of the base, and $M$ is the midpoint of $SO$. The moving point $P$ is on the base of the conical frustum (including the circumference). If $AM \perp MP$, find the length of the locus formed by point $P$.

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