
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 line $l$ are given by $\begin{cases} x=1-\frac{1}{2}t \\ y=\frac{\sqrt{3}}{2}t \end{cases}$, where $t$ is the parameter. With the origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis, a curve $C$ has the polar equation $\rho=6\cos \theta$.
(I) Write down the Cartesian equation of line $l$ and curve $C$;
(II) If $P$ is the point with Cartesian coordinates $(1,0)$, and $C$ intersects $l$ at points $A$ and $B$, find the value of $|PA|+|PB|$.

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