
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
Given the polar equation of curve $C$ is $\rho=4\sin \theta$, with the pole as the origin of the Cartesian coordinate system and the polar axis as the positive half-axis of $x$, establish the Cartesian coordinate system. The parametric equation of line $l$ is $\begin{cases} x= \frac{ \sqrt{2}}{2}t, \\ y=-4+ \frac{ \sqrt{2}}{2}t \end{cases}$ (where $t$ is the parameter), and point $P$ is a moving point on curve $C$, point $Q$ is a moving point on line $l$, find the minimum value of $|PQ|$.

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