
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
Find the perimeter of triangle $ABF_2$ if a line drawn through the focus $F_1$ of the ellipse $\frac{x^2}{36} + \frac{y^2}{25} = 1$ intersects the ellipse at points $A$ and $B$. $F_2$ is the other focus of the ellipse.

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