
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 $({ρ}^{2}\cos 2θ=9)$, and there is a point $P(2 \sqrt{3}, \dfrac{π}{6})$. Establish a rectangular coordinate system with the polar point $O$ as the origin and the positive half of the polar axis as the $x$-axis.

(I) Find the standard form of the parametric equation of line $OP$ and the rectangular coordinate equation of curve $C$;

(II) If line $OP$ intersects curve $C$ at points $A$ and $B$, find the value of $\dfrac{1}{\left|PA\right|}+ \dfrac{1}{\left|PB\right|}$.

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