
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 that ${F}_{1}$ and ${F}_{2}$ are the two foci of the ellipse $C: \frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$, and $P$ is a point on the ellipse $C$. If $\overrightarrow{P{F}_{1}} \perp \overrightarrow{P{F}_{2}}$, and the area of $\Delta P{F}_{1}{F}_{2}$ is $9$, then $b=$ _______ .

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