
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
On the number line, points $A$, $B$, and $C$ represent rational numbers $a$, $b$, and $c$, respectively, where $a = \left(-4\right)^{2} - 8$. Points $B$ and $C$ represent two numbers that are opposite to each other, and the distance between points $C$ and $A$ is $3$.  
$(1)$ Find the numbers represented by points $B$ and $C$;  
$(2)$ Calculate the value of $-a^{2} + b - c$.

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