
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
If 15 women leave, the remaining ratio of men to women is $2:1$. After this, if 45 men leave, the ratio of men to women becomes $1:5$. Calculate the initial number of women in the group.

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