
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 sequence $\{a_{n}\}$ satisfies $a_{1}=2$, ${a_{n+1}}=\frac{{2(n+2)}}{{n+1}}{a_n}$ ($n\in\mathbb{N}^*$). Find $\frac{{a_{2022}}}{{a_1+a_2+\cdots+a_{2021}}}$.

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