
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 that the cube root of $a-4$ is $1$, the arithmetic square root of $b$ is $2$, and the integer part of $\sqrt{11}$ is $c$.  
$(1)$ Find the values of $a$, $b$, and $c$;  
$(2)$ Find the square root of $2a-3b+c$.

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