
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
There are $n$ teams that need to hold a double round-robin tournament (each pair of teams competes twice, with each team having one match at their home field). Each team can play multiple away games in a week (from Sunday to Saturday). However, if a team has a home game in a particular week, they cannot have any away games scheduled in that week. Determine the maximum value of $n$ if all games can be completed within 4 weeks.

(Note: A match held at team A's field between teams A and B is considered a home game for team A and an away game for team B.)

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