
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
Let $P$ be a moving point on the ellipse $C: \frac{{x}^{2}}{7} + \frac{{y}^{2}}{3} = 1$, with $F_{1}$ and $F_{2}$ being the left and right foci, respectively. Extend $F_{1}P$ to point $Q$ such that $|PQ| = |PF_{2}|$. The equation of the trajectory of the moving point $Q$ is ____.

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