
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
Suppose there are 100 mutually hostile countries on Mars. To maintain peace, they decide to form several alliances, with the requirement that each alliance includes at most 50 countries, and every two countries must belong to at least one common alliance.
1. What is the minimum number of alliances required to meet the above requirements?
2. If there is an additional requirement that the union of any two alliances includes no more than 80 countries, what is the result?

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