
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 Brookside Intermediate School, there is an enthusiastic four-square league with twelve players, among them Alex and Martin. Each day during their break, the twelve students form two separate four-square games, each involving six players in no relevant order. Throughout an academic semester, each possible matchup of six players happens once. How many times did Alex play in the same game as Martin?

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