
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
A circle passes through the points (2,5) and (-2,1), and its center lies on the line y = $\frac{1}{2}$x.
(1) Find the standard equation of the circle;
(2) Find the minimum distance from the points on the circle to the line 3x - 4y + 23 = 0.

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