
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
Let $P$ be a point on the ellipse $\dfrac {x^{2}}{169}+ \dfrac {y^{2}}{144}=1$, and let $F_1$, $F_2$ be the foci of the ellipse. If $|PF_1|$ equals $4$, then find the value of $|PF_2|$.

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