
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 ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{5}=1$ with the right focal point $F$, where $B$ is a moving point on the ellipse, $\triangle FAB$ is an equilateral triangle, and $F$, $A$, $B$ are arranged in counterclockwise order, find the locus of point $A$.

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