
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 plane, establish a polar coordinate system with the origin O as the pole and the positive half of the x-axis as the polar axis. The polar equation of curve C is $\rho=4\cos\theta$. The parametric equation of line $l$ is
$$
\begin{cases}
x=-3+\frac{\sqrt{3}}{2}t,\\
y=\frac{1}{2}t
\end{cases}
$$
(where $t$ is the parameter).
1. Find the polar coordinates of the projection point P of the pole on line $l$.
2. Suppose that $M$ and $N$ are moving points on curve C and line $l$, respectively. Find the minimum value of $|MN|$.

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