
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
Four teams, including Quixajuba, are competing in a volleyball tournament where:

- Each team plays against every other team exactly once;
- Any match ends with one team winning;
- In any match, the teams have an equal probability of winning;
- At the end of the tournament, the teams are ranked by the number of victories.

a) Is it possible that, at the end of the tournament, all teams have the same number of victories? Why?

b) What is the probability that the tournament ends with Quixajuba alone in first place?

c) What is the probability that the tournament ends with three teams tied for first place?

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