
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 $f(x) = 4 \ln x - 2x^2 + 3ax,$
(1) When $a=1$, find the equation of the tangent line to the graph of $f(x)$ at the point $(1, f(1))$;
(2) If the function $g(x) = f(x) - 3ax + m$ has two zeros on the interval $\left[\frac{1}{e}, e\right]$, find the range of the real number $m$.

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