
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 that $F_{1}$ and $F_{2}$ are two foci of the ellipse $C$: $\frac{x^2}{3}+\frac{y^2}{2}=1$, and two moving points $P$ and $Q$ on the ellipse $C$ satisfy that the three points $P$, $Q$, and $F_{1}$ are collinear. Find the perimeter of $\triangle PQF_{2}$.

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