
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
Westvale Middle School has a dedicated four-square league with twelve players, including Michael and Sarah. Each recess, the twelve players are divided into two games, each consisting of six players in no particular order. Throughout the semester, each possible set of six players plays together exactly once. Determine how many times Michael played in the same game as Sarah.

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