
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 basketball tournament every two teams play two matches. As usual, the winner of a match gets  $2$  points, the loser gets  $0$ , and there are no draws. A single team wins the tournament with  $26$  points and exactly two teams share the last position with  $20$  points. How many teams participated in the tournament?

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