
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 hold a double round robin tournament with home and away games (each pair of teams plays 2 games, with each team having one home game). Each team can play multiple away games in a week (from Sunday to Saturday). However, if a team has a home game in a week, it cannot have any away games in that same week. If all games can be completed within four weeks, find the maximum value of $n$.

Note: A game between teams $A$ and $B$ held at $A$'s home venue is called a home game for $A$ and an away game for $B$.

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