
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
In the $1^{\mathrm{st}}$ grade, each child was asked to write down two numbers: the number of their male classmates and the number of their female classmates (in this order; the child did not count themselves). Each child wrote one number correctly, while the other number was off by exactly 4. Among the responses were: $(10,14),(13,11),(13,19)$. How many boys and how many girls are in the class?

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