
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
Given the function $f\left(x\right)=\sin \frac{{πx}}{3}$, a sequence $\{a_{n}\}$ satisfies $a_{1}=1$, and $a_{n+1}=(1+\frac{1}{n})a_{n}+\frac{1}{n}$ (where $n$ is a positive integer). Calculate $f(a_{2022})$.

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