
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
There are 33 students in a class. Before Christmas, they went to the forest with a forester to fill feeders. The girls took bundles of hay. The boys split into two groups: some took 4 bags of carrots and 3 bags of nuts, and the others took one bag of apples and one bag of nuts. The ratio of the number of girls, boys in the first group, and boys in the second group was the same as the ratio of the number of bags of nuts, apples, and carrots.

How many girls were there in the class, how many boys carried bags of carrots, and how many carried bags of apples?

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