
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
Connect the right focus \( F \) of the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\) with a moving point \( A \) on the ellipse, and construct a square \( FABC \) (with \( F, A, B, C \) arranged in a clockwise order). As point \( A \) moves around the ellipse once, find the equation of the trajectory of the moving point \( C \).

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