
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 $f(x)=x^{2}-ax+b$.

$(1)$ If the solution set of the inequality $f(x) < 0$ is $\{x|2 < x < 3\}$, find the solution set of the inequality $bx^{2}-ax+1 > 0$;

$(2)$ When $b=3-a$, for any $x \in (-1,0]$, $f(x) \geqslant 0$ holds, find the range of the real number $a$.

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