
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 the $n$th Fibonacci number where $G_1 = 1, G_2 = 1$, and $G_{n+1} = G_n + G_{n-1}$. Compute the value of
\[
\prod_{k = 1}^{50} \left( \frac{G_k}{G_{k+1}} - \frac{G_k}{G_{k+2}} \right) = \frac{G_x}{G_y}
\]
and determine the ordered pair $(x,y)$.

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