
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 three-square league, consisting of nine players, including Amy and Bob. Each day at recess, the nine players split into three three-square games, each with three players in no relevant order. Over the course of a semester, each possible match-up of three players occurs once. How many times did Amy play in the same game as Bob?

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