
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
Crestwood Middle School has a modified four-square league consisting of eight players, including Justin and Tim. Each day at recess, the eight players are split into two games, where one game has four players and the other game fluctuates between having three and four players depending on the day. Over a semester, each possible combination of players for a game with four players occurs once. How many times did Justin play in the same four-player game as Tim?

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