
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 equilateral cone \( SO \) with an axial cross-section \( SAB \) where \( SA = 2 \), and point \( M \) being the midpoint of \( SO \). A moving point \( P \) lies on the plane of the cone's base and the angle between \( MP \) and \( SA \) is \( 60^{\circ} \). In the plane of the cone's base, with \( AB \) as the \( x \)-axis and \( O \) as the origin, find the trajectory of point \( P \).

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