
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
Find the equation of the circle that passes through point A(2, -1), is tangent to the line x + y = 1, and has its center on the line y = -2x.

(I) Determine the standard equation of the circle.

(II) Calculate the length of the chord AB, where the circle from (I) intersects with the line 3x + 4y = 0.

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