
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 lottery ticket, it is required to mark 8 cells out of 64. What is the probability that after the draw, in which 8 cells out of 64 will also be chosen (all such possibilities are equally likely), it turns out that:
a) exactly 4 cells are guessed?
b) exactly 5 cells are guessed?
c) all 8 cells are guessed?

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