
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 quadratic function $f(x)=ax^{2}-bx+2$ where $a > 0$.
(1) If the solution set of the inequality $f(x) > 0$ is ${x|x > 2$ or $x < 1}$, find the values of $a$ and $b$.
(2) If $b=2a+1$, solve the inequality $f(x)\leqslant 0$ with respect to $x$.

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