
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]


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The 25 member states of the European Union set up a committee with the following rules:
1. The committee should meet daily;
2. At each meeting, at least one member state should be represented;
3. At any two different meetings, a different set of member states should be represented;
4. At the \( n \)th meeting, for every \( k < n \), the set of states represented should include at least one state that was represented at the \( k \)th meeting.

For how many days can the committee have its meetings?

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