
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 ${a}_{1}=1,{a}_{2}=2,{a}_{n+2}=\left\{\begin{array}{l}{a}_{n+1}-{a}_{n},{a}_{n}＜{a}_{n+1}\\{a}_{n}-{a}_{n+1},{a}_{n}≥{a}_{n+1}\end{array}\right.$, then the sum of the first $2023$ terms of $\{a_{n}\}$ is $S_{2023}=\_\_\_\_\_\_$.

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