
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 the algebraic expression $M=\left(a-b-1\right)x^{5}-7x^{2}+\left(a+3b\right)x-2$ is a quadratic polynomial in terms of $x$.  
$(1)$ If the solution to the equation in terms of $y$, $\left(3b-3a\right)y=ky-5$, is $y=1$, find the value of $k$.  
$(2)$ If the solution to the equation in terms of $y$, $\left(3b-3a\right)y=ky-5$, is a positive integer, find the integer value of $k$.

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