
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 Elementary School's four-square league has expanded to include 12 players, now including Emily along with Justin and Tim. Each day at recess, the twelve players split into two games, one with seven players and another with five players. Over a semester, each possible lineup of seven players for the larger game occurs once. How many times did Justin, Tim, and Emily play in the same seven-player game?

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