
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
It can be shown that for any positive integer \( n \),
\[
\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}^n = \begin{pmatrix} F_{n + 1} & F_n \\ F_n & F_{n - 1} \end{pmatrix},
\]
where \( F_n \) denotes the \( n \)th Fibonacci number.

Compute \( F_{1002} F_{1004} - F_{1003}^2 \).

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