
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
Greenfield Middle School has an active dodgeball league, consisting of twelve players, including Lucas and Molly. Each day at recess, the twelve players split into two dodgeball teams, 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 Lucas play in the same team as Molly?

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