
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 ray $3x - y = 0 (x \geqslant 0)$, is tangent to the line $x = 4$, and the chord intercepted by the line $3x + 4y + 10 = 0$ has a length of $4\sqrt{3}$.
(I) Find the equation of circle C;
(II) Points A(1, 1) and B(-2, 0). Point P moves on circle C. Find the maximum value of $|PA|^2 + |PB|^2$.

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