
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 function $f(x)=ax^{2}-(a+1)x+1$ where $(a\neq 0)$.
$(1)$ If $f(x)\leqslant 2$ always holds true for all $x$ in $\mathbb{R}$, find the range of values for the real number $a$.
$(2)$ Solve the inequality $f(x) < 0$ with respect to $x$.

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