
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 rectangular coordinate system $(xOy)$, the parametric equations of the curve $C$ are $\begin{cases} x=3\cos \alpha \ y=\sqrt{3}\sin \alpha \end{cases}$, where $\alpha$ is the parameter. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of the line $l$ is $\rho \cos (\theta + \dfrac{\pi }{3})=1$.

(1) Find the rectangular equation of $l$ and the ordinary equation of $C$;

(2) The line $l$ intersects the curve $C$ at points $A$ and $B$. Let point $P$ be a point on $C$ distinct from $A$ and $B$. When the area of $\triangle PAB$ is maximized, find the distance from point $P$ to $l$.

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