
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 the polar coordinate system, the equation of curve C is $\rho^2\cos2\theta=9$. Point P is $(2\sqrt{3}, \frac{\pi}{6})$. Establish a Cartesian coordinate system with the pole O as the origin and the positive half-axis of the x-axis as the polar axis.  
(1) Find the parametric equation of line OP and the Cartesian equation of curve C;  
(2) If line OP intersects curve C at points A and B, find the value of $\frac{1}{|PA|} + \frac{1}{|PB|}$.

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