
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 $E$: $\dfrac{x^{2}}{9}- \dfrac{y^{2}}{16}=1$ with its left and right foci being $F_{1}$ and $F_{2}$ respectively, and a point $P$ on the hyperbola $E$ such that $|PF_{1}|=3$, calculate the distance $|PF_{2}|$.

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