
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
On a certain planet, there are 100 countries. They all agree to form unions, each with a maximum of 50 countries, and that each country will be joining a number of unions, so that every two different countries will belong to the same union. At least how many unions must be formed?

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