
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
25 great circles on the sphere are in general position (in other words, at most two circles pass through any two points on the sphere). How many regions do they divide the sphere into?

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