
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 that $P$ and $Q$ are points on the line $\begin{cases} x=t \\ y=6-2t \end{cases} (t\text{ is a parameter})$ and the curve $C$: $\begin{cases} x=1+\sqrt{5}\cos\theta \\ y=-2+\sqrt{5}\sin\theta \end{cases} (\theta\text{ is a parameter})$, find the minimum value of $|PQ|$.

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