
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
$(1)$ Given $x$ and $y$ satisfy: $|x-2|+(y+3)^{2}=0$, where $z$ is the largest negative integer, simplify and find the value of $2(x^{2}y+xyz)-3(x^{2}y-xyz)-4x^{2}y$;<br/>$(2)$ Given $a+b=-7$, $ab=10$, find the value of the algebraic expression $\left(3ab+6a+4b\right)-\left(2a-2ab\right)$.

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