
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
The game show "Island Challenge" involves 20 contestants split into two tribes of 10 each. In the season opener, three contestants decide to leave the show. Assuming an equal probability for each contestant to be one of the three who leave, and that the quitting of any contestant is independent of the others, what is the probability that all three quitters come from the same tribe?

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