
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
Suppose that  $m$  and  $n$  are relatively prime positive integers with  $A = \tfrac mn$ , where
\[ A = \frac{2+4+6+\dots+2014}{1+3+5+\dots+2013} - \frac{1+3+5+\dots+2013}{2+4+6+\dots+2014}. \] Find  $m$ . In other words, find the numerator of  $A$  when  $A$  is written as a fraction in simplest form.

*Proposed by Evan Chen*

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