
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
15 billiard balls are placed flat on an equilateral triangle frame, and its inner perimeter is 876 mm. Calculate the radius of each billiard ball.

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