
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
Consider real numbers  $A$ ,  $B$ , \dots,  $Z$  such that \[
  EVIL = \frac{5}{31}, \;
  LOVE = \frac{6}{29}, \text{ and }
  IMO  = \frac{7}{3}.
\] If  $OMO = \tfrac mn$  for relatively prime positive integers  $m$  and  $n$ , find the value of  $m+n$ .

*Proposed by Evan Chen*

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