
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 that $\left(a+b\right)y^{2}-{y}^{\frac{1}{3}a+2}+5=0$ is a linear equation in terms of $y$.<br/>$(1)$ Find the values of $a$ and $b$;<br/>$(2)$ If $x=a$ is a solution to the equation $\frac{x+2}{6}-\frac{x-1}{2}+3=x-\frac{2x-m}{6}$, find the value of $|a-b|-|b-m|$.

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