
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 $l$ is an asymptote of the hyperbola $C$: $\dfrac{x^{2}}{2}- \dfrac{y^{2}}{4}=1$, and $P$ is a point on $l$, $F_{1}$ and $F_{2}$ are the two foci of $C$. If $\overrightarrow{PF_{1}} \cdot \overrightarrow{PF_{2}}=0$, calculate the distance from $P$ to the $x$-axis.

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