
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 points P and Q lie on the line $\begin{cases} x=t \\ y=15-2t \end{cases}$ (with $t$ as the parameter) and curve C: $\begin{cases} x=1+ \sqrt {5}\cos\theta \\ y=-2+ \sqrt {5}\sin\theta \end{cases}$ (with $\theta$ as the parameter) respectively, find the minimum value of $|PQ|$.

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