
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
In a round-robin tournament involving six teams, teams A and B each played 3 matches, teams C and D each played 4 matches, and team E played 2 matches. It is also known that team A did not play against team C, and team B did not play against team D. Calculate the number of matches that team F played in the first week of the competition.

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