
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 planet $X$, there are 100 alien countries with conflicts among them. To avoid a world war, these countries organize themselves into military alliance groups for mutual protection. We know that the alliances follow these rules:

1) No alliance contains more than 50 countries.
2) Any two countries belong to at least one alliance.

a) Is it possible for a country to participate in fewer than three military alliances?

b) What is the minimum number of alliances needed to satisfy these two conditions?

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