
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 round-robin football tournament, there are $n$ teams participating. Among them, 2 teams played 3 matches each and then withdrew from the competition. These two teams did not play against each other. In total, 34 matches were played by the end of the tournament. Find the value of $n$.

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