
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 has an active four-square league, consisting of twelve players, including Michael and Sarah. Each day at recess, the twelve players split into two four-square games, each with six players in no relevant order. Over the course of a semester, each possible match-up of six players occurs once. How many times did Michael play in the same game as Sarah?

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