
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
In the Cartesian coordinate system, there are several points with integer abscissas, in the order of $\left(0,0\right)$, $\left(1,1\right)$, $\left(2,0\right)$, $\left(3,-1\right)$, $\left(4,0\right)$, $\left(5,1\right)$, $\left(6,0\right)$, $\left(7,-1\right)$, $\left(8,0\right)$, $\ldots $, according to this pattern, the coordinates of the $2023$rd point are ______.

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