
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 $|2a+b|$ and $\sqrt{3b+12}$ are opposite in sign.<br/>$(1)$ Find the square root of $2a-3b$;<br/>$(2)$ Solve the equation $ax^{2}+4b-2=0$ in terms of $x$.

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