
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 $f(x)=a\ln x+bx^{2}$, the equation of the tangent line at point $P(1,f(1))$ on the graph of the function is $2x-y-3=0$.

(I) Find the analytic expression of the function $y=f(x)$;

(II) For the function $g(x)=f(x)+m-\ln 4$, if the equation $g(x)=0$ has exactly two solutions in the interval $[\frac{1}{e}, 2]$, find the range of the real number $m$.

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