
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:
$$
\begin{array}{l}
f(n+3)=\frac{f(n)-1}{f(n)+1}, \\
f(1) \neq 0 \text{ and } f(1) \neq \pm 1.
\end{array}
$$

Determine the value of \( f(11) f(2021) \).

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