
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 hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{6} = 1$ with left and right foci $F_1$ and $F_2$, let line $l$ pass through $F_1$ and intersect the left branch of the hyperbola at points $A$ and $B$. Find the minimum value of $|AF_2| + |BF_2|$.

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