
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
The Fibonacci numbers are defined by \( F_{1} = F_{2} = 1 \) and \( F_{n+2} = F_{n+1} + F_{n} \) for \( n \geq 1 \). The Lucas numbers are defined by \( L_{1} = 1, L_{2} = 2 \), and \( L_{n+2} = L_{n+1} + L_{n} \) for \( n \geq 1 \). Calculate \(\frac{\prod_{n=1}^{15} \frac{F_{2 n}}{F_{n}}}{\prod_{n=1}^{13} L_{n}}\).

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