
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(3, 3) and B(2, 4), and the center of the circle C is on the line $y=3x-5$.  
(1) Find the standard equation of circle C;  
(2) Let P(-m, 0) and Q(m, 0) where $m>0$. If there exists a point M on circle C such that point M is also on the circle with diameter PQ, find the range of values for the real number m.

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