
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 $a$ and $b$ be non-zero real numbers such that
\[
\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{1}{b}} = 1001.
\]
Determine the value of $\frac{a+b}{a-b}$.
A) $-1001$
B) $\frac{-1}{1001}$
C) $\frac{1}{1001}$
D) $1$
E) $1001$

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