
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 should be represented;
3) at any two different meetings, a different set of member states should be represented;
4) at  $n^{th}$  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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