
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

A boy and a girl: We assume that the birth of a girl and a boy are equally probable. It is known that a certain family has two children.

a) What is the probability that one of them is a boy and the other is a girl?

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

c) Additionally, it is known that the boy was born on 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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