
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
In a survival challenge event, 20 participants are divided into two groups of 10 each. During the challenge, three participants decide to leave the event. Assuming each participant has an equal chance of being one of the quitters and the quitting of one participant does not influence others, calculate the probability that all three quitters come from the same group.

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