
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
Within the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$, there is a point $M(P, 0)$ where $0 < P < a$. A moving point $Q$ on the ellipse is such that the vector $\overrightarrow{MQ}$ is rotated $90^\circ$ clockwise around point $M$ to become $\overrightarrow{MP}$. Find the equation of the locus of point $P$.

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