
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 that the center of circle C lies on the line x-2y=0 and passes through points M(0,-1) and N(1,6).
(I) Find the equation of circle C;
(II) Given points A(1,1) and B(7,4), if P is a moving point on circle C, find the range of values for $|PA|^2+|PB|^2$.

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