
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 $300$ students at Lincoln Middle School with a boys to girls ratio of $3:2$, and there are $240$ students at Jackson Middle School with a boys to girls ratio of $2:3$. A sports event is held where all students from both schools participate, along with $150$ students from Franklin Middle School with a boys to girls ratio of $1:1$. What fraction of the students at the sports event are boys?
A) $\frac{351}{690}$
B) $\frac{5}{9}$
C) $\frac{117}{230}$
D) $\frac{1}{2}$
E) $\frac{3}{4}$

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