
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
A cone has an axis section $SAB$ that is an equilateral triangle with side length $2$. $O$ is the center of the base, $M$ is the midpoint of $SO$, and moving point $P$ is inside the base circle (including the circumference). If $AM \perp MP$, then the length of the trajectory formed by point $P$ is _______.

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