
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 $\frac{x^{2}}{25} - \frac{y^{2}}{9} = 1$ with two foci $F\_1$ and $F\_2$, if the distance between a point $P$ on the hyperbola and focus $F\_1$ is $12$, then the distance between point $P$ and focus $F\_2$ is ___.

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