
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 reality game show Survivor is played with 20 people, now divided into two tribes of 10 each. During the first episode, three people get homesick and quit. Assuming every person has an equal chance of being one of the quitters and that the quitting of one person is independent of the quitting of any other person, what is the probability that all three people who quit are from the same tribe?

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