
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 school is holding a table tennis team competition, which adopts a $5$-game $3$-win system. Each game is a singles match. If a team wins $3$ games first, the competition ends. Each team is required to send $3$ athletes to participate, and each athlete can participate in at most $2$ games in the team competition. In the first $3$ games, each athlete plays once. If the outcome is not determined after the first $3$ games, the athletes who played in the first or second game will participate in the subsequent games.<br/>$(Ⅰ)$ If a team selects $3$ out of $5$ athletes to participate in this team competition, how many possible lineups are there for the first $3$ games of the team? <br/>$(Ⅱ)$ It is known that athletes A, B, and C from a team participate in this team competition.<br/>① If the outcome is determined after $3$ games, list all possible lineups for the team; <br/>② If the outcome is determined after $4$ or $5$ games, how many possible lineups are there for the team?

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