
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

The probability that a person's birthday falls in a specific month of the year is approximately the same for all 12 months. What is the probability that:

a) In a given company of 12 people, all 12 birthdays fall in different months?

b) In a given company of 6 people, all birthdays fall in some two months?

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