
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 $f(x)=ax^{2}+x-x\ln x(a > 0)$.
(1) If the function satisfies $f(1)=2$, and $f(x)\geqslant bx^{2}+2x$ always holds true in the domain, find the range of values for the real number $b$;
(2) If the function $f(x)$ is a monotonic function in the domain, find the range of values for the real number $a$;
(3) When $\frac {1}{e} < x < y < 1$, compare the size of $\frac {y}{x}$ with $\frac {1+\ln y}{1+\ln x}$.

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