
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 a circle C that passes through points A(-2, 1) and B(5, 0), and the center of the circle C is on the line $y=2x$.  
(1) Find the standard equation of circle C;  
(2) Let the moving line $l: (m+2)x + (2m+1)y - 7m - 8 = 0$ intersect circle C at points P and Q. Find the minimum value of $|PQ|$.

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