
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
A certain city is organizing a volleyball invitational tournament, where each pair of teams must play against each other. According to the conditions of the venue and time, the tournament is planned for $7$ days with $4$ games scheduled each day. How many teams should the organizers invite to participate?

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