
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
Numbers from 1 to 200 are placed in random order on a circle so that the distances between adjacent numbers on the circle are equal.

For any given number, the following is true: if we consider the 99 numbers situated clockwise from it and the 99 numbers situated counterclockwise from it, both groups will contain an equal number of numbers that are smaller than the given number.

What number is opposite the number 113?

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