
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
Twelve students from an olympiad class went out to play soccer every day after math class, forming two teams of six players each and playing against each other. Each day they formed two different teams from those formed on previous days. At the end of the year, they found that each group of five students had played together on the same team exactly once. How many different teams were formed throughout the year?

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