
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 point $O$ is the coordinate origin, and point $P$ lies on the hyperbola $x^{2}- \frac{y^{2}}{b^{2}}=1 (b > 0)$. Two lines parallel to the asymptotes pass through point $P$ and intersect the asymptotes at points $A$ and $B$. Find the eccentricity of the hyperbola given that the area of the parallelogram $PAOB$ is $1$.

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