
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 the origin and its center is on the line $y=2x$, the line $x+y-3=0$ intersects circle C at points A and B, and $\overrightarrow{OA} \cdot \overrightarrow{OB} = 0$,

(1) Find the equation of circle C;  
(2) If $M(0, 5)$, and P is a moving point on the circle, find the range of values for the slope of line MP.

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