
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 7n teams participating in a double round-robin tournament (each pair of teams plays two matches, one home and one away). Each team can play multiple matches within a week (from Monday to Sunday). If a team has a home match in a given week, it cannot have an away match in the same week. If all matches can be completed within 4 weeks, find the maximum value of n.

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