
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 equation of line $l$ is 
$$
\begin{cases} 
x=3+t\cos\phi \\
y=1+t\sin\phi 
\end{cases}
$$
($t$ is the parameter). In the polar coordinate system with the origin as the pole and the positive half of the x-axis as the polar axis, the equation of circle $C$ is $\rho=4\cos\theta$.

(I) Find the standard equation of $l$ and the Cartesian coordinate equation of $C$;

(II) When $\phi \in (0, \pi)$, line $l$ intersects with circle $C$ at points $P$ and $Q$. Find the minimum value of $|PQ|$.

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