
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
Determine the least integer  $k$  for which the following story could hold true:
In a chess tournament with  $24$  players, every pair of players plays at least  $2$  and at most  $k$  games against each other. At the end of the tournament, it turns out that every player has played a different number of games.

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