
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
Define: On the number line, the distance from the point representing the number $a$ to the point representing the number $1$ is called the absolute value of $a$ with respect to $1$.  
$(1)$ The absolute value of $-1$ with respect to $1$ is ______;  
$(2)$ If the absolute value of $a$ with respect to $1$ is $2023$, then the value of $a$ is ______.

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