
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 $f(x) = 2(x^2 - 2ax)\ln x - x^2 + 4ax + 1$,  
(1) When $a=0$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(e, f(e))$ (where $e$ is the base of the natural logarithm);  
(2) Determine the intervals of monotonicity for the function $f(x)$.

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