
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
Given that $40\%$ of the group are girls, $30\%$ of the group are girls after two girls leave and two boys arrive, and the total number of people in the group remains constant, calculate the initial number of girls in the group.

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