
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 three simplest proper fractions with their numerators in the ratio $3: 2: 4$ and their denominators in the ratio $5: 9: 15$. When these three fractions are added together and then reduced to simplest form, the result is $\frac{28}{45}$. What is the sum of the denominators of these three fractions?

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