
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
Given \(\frac{2+4+6+8}{1+3+5+7}-\frac{1+3+5+7}{2+4+6+8}=\frac{m}{n}\), where \(\mathbf{m}\) and \(\mathbf{n}\) are two coprime positive integers, find \(10m+n\).

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