
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
Consider the function $f(x)=\frac{1}{2} ax^{2}-(1+a)x+\ln x$ where $a\geqslant 0$.

(1) Discuss the monotonicity of the function $f(x)$;

(2) When $a=0$, the equation $f(x)=mx$ has a unique real solution in the interval $[1,e^{2}]$. Find the range of the real number $m$.

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