
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 volleyball tournament with 5 teams, where there are no ties, each team plays against every other team. The team that finished in 1st place won all their matches. The teams that finished in 2nd and 3rd places each won exactly two matches. In case of equal points, the ranking is determined by the result of the match between the teams. How many matches did the team that finished in last place win? Determine which team won against which other teams.

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