
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
When \( n \) is a positive integer, the function \( f \) satisfies
\[ f(n+3) = \frac{f(n) - 1}{f(n) + 1}, \]
with \( f(1) \neq 0 \), and \( f(1) \neq \pm 1 \).

Compute \( f(1) f(2023) \).

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