
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
The polar equation of the trajectory where point $P$ is located is $\rho=2\cos \theta$, and the parametric equation of the trajectory where point $Q$ is located is $\begin{cases} x=3t \\ y=\sqrt {3}+\sqrt {3}t \end{cases}$ (with $t$ as the parameter). Find the minimum value of $|PQ|$.

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