
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 a sequence $\{a_{n}\}$, where $a_{1}=1$, $a_{n} \gt 0$, and the sum of the first $n$ terms is $S_{n}$. If ${a_n}=\sqrt{{S_n}}+\sqrt{{S_{n-1}}}$ for $n \in \mathbb{N}^{*}$ and $n \geq 2$, then the sum of the first 2022 terms of the sequence $\left\{{\frac{1}{{{a_n}{a_{n+1}}}}}\right\}$ is ____.

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