
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 a popular dodgeball league, consisting of twelve players, including Sarah and Mia. Each day at recess, the twelve players split into two dodgeball games, each with six players in no particular order. Over the course of a semester, each possible matchup of six players occurs once. How many times did Sarah play in the same game as Mia?

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