
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
In a polar coordinate system, the equation of curve \(C\) is \({\rho}^{2}\cos 2\theta = 9\), and we are considering the point \(P(2\sqrt{3},\frac{\pi}{6})\). Let \(O\) be the pole and the positive x-axis the polar axis to establish the Cartesian coordinate system.

(1) Find the standard form of the parametric equation of the line \(OP\) and the Cartesian equation of the curve \(C\);

(2) If the line \(OP\) intersects the curve \(C\) at points \(A\) and \(B\), calculate the value of \(\frac{1}{|PA|}+\frac{1}{|PB|}\).

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