
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
Let \( n > 1 \) and \( m \) be natural numbers. A parliament consists of \( m n \) members who have formed \( 2 n \) commissions, so that:

1. Each commission consists of \( m \) deputies.
2. Each Member of Parliament is a member of exactly 2 commissions.
3. No two commissions have more than one joint member.

Determine the largest possible value of \( m \) as a function of \( n \) so that this is possible.

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