
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 $f(x)=a\ln x-bx^{2},a,b\in R.$ If the equation of the tangent line to $f(x)$ at the point $(2,f(2))$ is $3x-2y-2-2\ln 2=0$.

(1) Find the values of $a$ and $b$;

(2) Find the maximum value of $f(x)$ on $\left[\dfrac{1}{e}, \sqrt{e}\right]$.

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