
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 equation of a hyperbola $\frac{x^{2}}{a^{2}}- \frac{y^{2}}{b^{2}}=1$, points $A$ and $B$ are on the right branch of the hyperbola. The line segment $AB$ passes through the right focus $F_2$ of the hyperbola, with $|AB|=m$. $F_1$ is the other focus. Calculate the perimeter of $\triangle ABF_1$.

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