
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
Reading comprehension: If $x$ satisfies $\left(210-x\right)\left(x-200\right)=-204$, find the value of $\left(210-x\right)^{2}+\left(x-200\right)^{2}$. Solution: Let $210-x=a$, $x-200=b$, then $ab=-204$, and $a+b=210-x+x-200=10$. Since $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$, we have $a^{2}+b^{2}=\left(a+b\right)^{2}-2ab=10^{2}-2\times \left(-204\right)=508$. Therefore, the value of $\left(210-x\right)^{2}+\left(x-200\right)^{2}$ is $508$. Based on the information, please complete the solution process for the following question: If $x$ satisfies $\left(2024-x\right)^{2}+\left(2022-x\right)^{2}=4038$, find the value of $\left(2024-x\right)\left(2022-x\right)$.

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