
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
On a soccer tournament with  $n\ge 3$  teams taking part, several matches are played in such a way that among any three teams, some two play a match. $(a)$  If  $n=7$ , find the smallest number of matches that must be played. $(b)$  Find the smallest number of matches in terms of  $n$ .

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