
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 (each pair of teams plays two matches, each having a home match). Each team can play multiple away matches in a week (from Sunday to Saturday). However, if a team has a home match in a given week, no away matches can be scheduled for that team in that week. If all matches are to be completed within 4 weeks, find the maximum possible value of $n$.
(Note: A match held at team A's venue between team A and team B is considered a home match for team A and an away match for team B.)

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