
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
A student is working on a math problem. Given two polynomials $A$ and $B$, where $B=3x^{2}y-2xy+x+2$, find $A+B$. The student mistakenly calculated $A-B$ instead of $A+B and obtained the answer $6x^{2}y+4xy-2x-1$.<br/>$(1)$ Please find the correct answer for $A+B$ for this student;<br/>$(2)$ When $x$ takes any numerical value, and the value of $A-3B$ is a constant, find the value of $y$.

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