
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
For a number $x$, we use $\left(x\right]$ to represent the largest integer less than $x$, for example: $\left(1.6\right]=1$, $\left(-4\right]=-5$.  
① Fill in the blanks: $(0 ]=\_\_\_\_\_\_,(-2023 ]=\_\_\_\_\_\_$;  
② If $|\left(x\right]-3|=6$, then the range of values for $x$ is ______.

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