
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
Given $|a|=4$, $b$ is the square root of $9$, and $c$ is the cube root of $-8$.  
$(1)$ Find the values of $a$, $b$, and $c$;  
$(2)$ If $a > b > c$, find the integer part of $\sqrt{a+b+c}$.

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