
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 hyperbola $\frac{x^2}{a^2} - y^2 = 1$, and point $P$ lies on this hyperbola such that $\overrightarrow{PF\_1} \cdot \overrightarrow{PF\_2} = 0$. If the eccentricity of this hyperbola is equal to $\frac{\sqrt{5}}{2}$, find the distance from point $P$ to the $x$-axis.

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