
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 \( F_{n} = F_{n-1} + F_{n-2} \) for \( n \geq 3 \). If the number
\[ \frac{F_{2003}}{F_{2002}} - \frac{F_{2004}}{F_{2003}} \]
is written as a fraction in lowest terms, what is the numerator?

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