
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
Find all functions $f: \mathbb{N}^* \rightarrow \mathbb{N}^*$ such that $\forall n \geq 1$,

$$
\begin{gathered}
\text { (i) } f(n) + f(n+1) = f(n+2) f(n+3) - 11 \\
\text { (ii) } f(n) \geq 2
\end{gathered}
$$

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