
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 $\rho^{2}\cos 2\theta=9$. Point $P(2 \sqrt {3}, \frac {\pi}{6})$ is given. 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}
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