
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 $f(x)=a\ln x-bx^{2}$, where $a,b\in\mathbb{R}$.

(I) If the function $f(x)$ is tangent to the line $y=-\frac{1}{2}$ at $x=1$:

1. Find the values of the real numbers $a$ and $b$.
2. Find the maximum value of the function $f(x)$ on the interval $[\frac{1}{e},e]$ ($e$ is the base of the natural logarithm).

(II) When $b=0$, if the inequality $f(x)\geqslant m+x$ holds for all $a\in[0,\frac{3}{2}]$, $x\in(1,e^{2}]$ ($e$ is the base of the natural logarithm), find the range of values for the real number $m$.

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