
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 320 students at Maplewood Middle School, where the ratio of boys to girls is 3:5, and 240 students at Brookfield Middle School, where the ratio of boys to girls is 5:3. A third school, Pinehurst Middle School, which has 400 students, joins them with a ratio of boys to girls being 1:1. Determine the fraction of the students at the combined event that are girls.

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