
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 Cartesian coordinate system $xOy$, the parametric equations of the line $l$ are $\left\{\begin{array}{l}{x=2+\frac{\sqrt{3}}{2}t}\\{y=\frac{1}{2}t}\end{array}\right.$ (where $t$ is a parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of the $x$-axis as the polar axis. The polar coordinate equation of the curve $C$ is $\rho ^{2}(\cos ^{2}\theta +9\sin ^{2}\theta )=9$.  
$(Ⅰ)$ Find the general equation of the line $l$ and the Cartesian equation of the curve $C$;  
$(Ⅱ)$ If the line $l$ intersects the curve $C$ at points $M$ and $N$, and $P(2,0)$, find the value of $|PM|+|PN|$.

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