
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
In the games for the USSR football cup, after the qualifying rounds, the teams are divided into two groups of equal size by lot. In each group, the winner is determined, and the winners of both groups meet in the cup final. Suppose the total number of teams that passed the qualifying rounds is 20.

a) What is the probability that the two strongest teams will end up in different groups?

b) What is the probability that the four strongest teams will end up in the same group? What is the probability that for two consecutive years, the four strongest teams will end up in the same group?

c) What is the probability that the four strongest teams will be divided into two different groups, with two in each group?

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