
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 function  $f$ , with domain on the set of non-negative integers, is defined by the following : $\bullet$   $f (0) = 2$  $\bullet$   $(f (n + 1) -1)^2 + (f (n)-1) ^2 = 2f (n) f (n + 1) + 4$ , taking  $f (n)$  the largest possible value.
Determine  $f (n)$ .

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