
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 algebraic expressions $A=2x^{2}-2x-1$, $B=-x^{2}+xy+1$, $M=4A-\left(3A-2B\right)$. Find the value of algebraic expression $M$ when $(1)$ $\left(x+1\right)^{2}+|y-2|=0$. $(2)$ If the value of algebraic expression $M$ is independent of $x$, find the value of $y$.

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