
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 $f(x)=x^{2}-(2a+1)x+a\ln x(a\in R)$.
(1) If $f(x)$ is a monotonic function on the interval $[1,2]$, find the range of values for the real number $a$;
(2) Given the function $g(x)=(1-a)x$, if there exists $x_{0}\in[1,e]$ such that $f(x_{0})\geqslant g(x_{0})$ holds, find the range of values for the real number $a$.

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