
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 the equation of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ with $a > b > 0$, the focal distance $c$, and the eccentricity $e$. Let $B(0, -b)$ be one endpoint of the minor axis of the ellipse. An isosceles triangle $\triangle B M N$ with $B$ as the vertex is inscribed in the ellipse, with $P$ being the midpoint of the base $MN$. Determine the locus of point $P$.

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