
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
Let \( m \) and \( n \) be two positive integers that satisfy
$$
\frac{m}{n}=\frac{1}{10 \times 12}+\frac{1}{12 \times 14}+\frac{1}{14 \times 16}+\cdots+\frac{1}{2012 \times 2014}
$$
Find the smallest possible value of \( m+n \).

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