
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 $f(x) = a \ln x - bx^2 + 1 (x > 0)$, if the equation of the tangent line to the function $f(x)$ at $x = 1$ is $6x - 2y - 5 = 0$.

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

(2) Find the maximum value of the function $f(x)$ on the interval $\left[ \frac{1}{e}, e^2 \right]$.

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