
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
Assume that the birth of a girl and a boy are equally likely. It is known that there are two children in a certain family.

a) What is the probability that they have one boy and one girl?

b) It is further known that one of the children is a boy. What is the probability now that the family has one boy and one girl?

c) It is further known that the boy was born on a Monday. What is the probability now that the family has one boy and one girl?

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