
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 that $m$ and $n$ are opposite numbers, and $m \neq n$, $p$ and $q$ are reciprocal numbers. Find the value of $\frac{m+n}{m}+2pq-\frac{m}{n}$.  
$(1)$ Find the value of $\frac{m+n}{m}+2pq-\frac{m}{n}$.  
$(2)$ Lulu, who loves thinking, found the condition $m \neq n$ to be redundant. Do you think Lulu's idea is correct? Why?

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