
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 $\begin{cases} x=t \\ y=6-2t \end{cases}$ (where $t$ is a parameter) and the curve $C$: $\begin{cases} x=1+ \sqrt {5}\cos \theta \\ y=-2+ \sqrt {5}\sin \theta \end{cases}$ (where $\theta$ is a parameter) respectively, find the minimum value of $|PQ|$.

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