
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]


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Pedro decided to take all of his children, boys and girls, to an ice cream parlor called Sorvete Matemático. In the ice cream parlor, there are 12 different flavors of ice cream, and each child ordered a combo with 3 scoops of ice cream. After leaving the ice cream parlor, Pedro realized that, in total, exactly two scoops of each available flavor were ordered.

a) Knowing that Pedro did not have any ice cream, what is the total number of his children (boys and girls)?

b) Pedro looked more closely at the flavors each child ordered and noticed that no flavor was chosen by both a boy and a girl, meaning if a boy chose a flavor, no girl chose that same flavor. Knowing that at least one of his children is a boy and that he has more daughters than sons, determine the number of his daughters.

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