
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
$n$ teams are to have a double round-robin tournament (each team plays every other team twice, once at home and once away). Each team can play multiple away games in a week (from Sunday to Saturday), but if they have a home game in a week, they cannot have any away games that week. If all games can be completed within 4 weeks, find the maximum value of $n$. Note: A game held at team A's venue between teams A and B is called a home game for team A and an away game for team B.

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