
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 $P(2, f(2))$ on the graph is $y = -3x + 2\ln2 + 2$.  
(1) Find the values of $a$ and $b$;  
(2) If the equation $f(x) + m = 0$ has two distinct real roots within the interval $\left[ \frac{1}{e}, e \right]$ (where $e$ is the base of the natural logarithm), find the range of values for $m$.

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