
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
The numerators of three fractions are proportional to the numbers \(1, 2, 5\), and the denominators are proportional, respectively, to the numbers \(1, 3, 7\). The arithmetic mean of these fractions is \( \frac{200}{441} \). Find these fractions.

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