
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 $m\neq 0$, $n\neq 0$, and $m-n=\frac{1}{2}$, find the value of the algebraic expression $\frac{{m^2}-{n^2}}{{2{m^2}+2mn}}÷({m-\frac{{2mn-{n^2}}}{m}})$.

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