
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
Fifteen girls are standing around a circle. A ball is thrown in a clockwise direction. The first girl, Bella, starts with the ball, skips the next four girls, and throws it to the sixth girl. This sixth girl then continues the pattern by skipping the next four girls. This pattern continues until ten throws are made; after that, the ball skips only two girls between throws. If this throwing pattern continues, how many total throws are necessary for the ball to return to Bella?

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