
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
At Maplewood Middle School, there’s a popular six-square league with twelve players, including Justin and Tim. Every month, the twelve players are split into two six-square games, each with six players in no particular order. Throughout the school year, each possible group of six players is formed once. How many times did Justin and Tim end up playing in the same game?

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