
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 $F_n$ be the $n$th Fibonacci number, defined as usual by $F_1 = F_2 = 1$ and $F_{n+1} = F_n + F_{n-1}$. Determine the value of the product 
\[
\prod_{k = 3}^{150} \left( \frac{F_k}{F_{k - 2}} - \frac{F_k}{F_{k + 2}} \right).
\]
Express your answer as $\frac{F_a}{F_b}$ for some positive integers $a$ and $b.$

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