
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 $C:\frac{x^{2}}{6}+\frac{y^{2}}{2}=1$ with left and right foci $F_1$ and $F_2$, respectively, a line $l$ passes through point $F_1$ and intersects ellipse $C$ at points $A$ and $B$. Calculate the perimeter of triangle $\Delta ABF_2$.

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