
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 sphere with radius 2 is intersected by a plane that is at a distance of 1 from the center. Find the length of the shortest path on the surface of the sphere between the two most distant points of the intersection.

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