
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 intersects the line $l_1: x - 6y - 10 = 0$ at point P(4, -1) and the center of the circle lies on the line $l_2: 5x - 3y = 0$.
(I) Find the equation of the circle;
(II) Find the length of the shortest chord that the circle cuts off from lines passing through the origin.

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