
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  $f:\mathbb{N} \rightarrow \mathbb{N}$  verifies: $1) f(n+2)-2022 \cdot f(n+1)+2021 \cdot f(n)=0, \forall n \in \mathbb{N};$  $2) f(20^{22})=f(22^{20});$  $3) f(2021)=2022$ .
Find all possible values of  $f(2022)$ .

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