
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 $F_{1}$ and $F_{2}$ be the left and right foci of the hyperbola $x^{2}- \frac {y^{2}}{9}=1$, respectively. Point $P$ is on the hyperbola, and $\overrightarrow{PF_{1}} \cdot \overrightarrow{PF_{2}}=0$. Find the value of $|\overrightarrow{PF_{1}}+ \overrightarrow{PF_{2}}|$.

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