
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
The length of the real axis and the focal distance of the hyperbola $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ are exactly the roots of the function $y=x^2-6x+8$. The asymptotes of the hyperbola intersect the parabola $y^2=(b^2-a^2)x$ at points $O$, $P$, and $Q$. Then, the area of $\triangle POQ$ is __________.

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