
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 ellipse $\frac{{x}^{2}}{16}+\frac{{y}^{2}}{9}=1$ with left and right foci ${F}_{1}$ and ${F}_{2}$ respectively, point $P$ lies on the ellipse, and if $P{F}_{1} \perp P{F}_{2}$, find the distance from point $P$ to the $x$-axis.

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