
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 $A=3x^{2}-x+2y-4xy$, $B=2x^{2}-3x-y+xy$.

$(1)$ Simplify $2A-3B$.

$(2)$ When $x+y=\frac{6}{7}$ and $xy=-1$, find the value of $2A-3B$.

$(3)$ If the value of $2A-3B$ is independent of the value of $y$, find the value of $2A-3B$.

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