
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
Point P is on circle $C_1$ given by the equation $(x-4)^2+(y-2)^2=9$, and point Q is on circle $C_2$ given by the equation $(x+2)^2+(y+1)^2=4$. Find the minimum value of $|\overrightarrow{PQ}|$.

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