
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
 $30$  volleyball teams have participated in a league.  Any two teams have played a match with each other exactly once. At the end of the league, a match is called **unusual** if at the end of the league, the winner of the match have a smaller amount of wins than the loser of the match. A team is called **astonishing** if all its matches are **unusual** matches.
Find the maximum number of **astonishing** teams.

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