
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 $G_n$ be defined as $G_1 = 1, G_2 = 2$, and $G_{n+1} = G_n + G_{n-1}$. Compute the product
\[
\prod_{k=2}^{50} \left( \frac{G_k}{G_{k-1}} - \frac{G_k}{G_{k+1}} \right)
\]
and express it as $\frac{G_c}{G_d}$ for some integers $c$ and $d$.

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