
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
Let the function be $y=ax^{2}+\left(b-2\right)x+3$<br/>$(1)$ If the solution set of the inequality $y \lt 0$ is $\{x\left|\right.1 \lt x \lt 3\}$, find the values of $a$ and $b$;<br/>$(2)$ If $a \gt 0$ and $b=-2a$, find the solution set of the inequality $y\leqslant -1$.

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