
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
Consider a point $P$ on the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$. If the distance between point $P$ and point $(5,0)$ is $15$, then the distance between point $P$ and point $(-5,0)$ is \_\_\_\_\_\_.

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