
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 center of the hyperbola is at the origin \( O \), with its foci on the \( x \)-axis. A line passing through the right focus of the hyperbola with a slope of \( \sqrt{\frac{3}{5}} \) intersects the hyperbola at points \( P \) and \( Q \). If \( P O \perp O Q \) and \(|P Q| = 4\), find the equation of the hyperbola.

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