
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 curve $C$: $\frac{x^2}{3} - y^2 = 1$ with left and right foci $F_1F_2$, a line passing through point $F_2$ intersects the right branch of curve $C$ at points $P$ and $Q$, where the x-coordinate of point $P$ is $2$. Calculate the perimeter of $PF_1Q$.

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