
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 $f(x) = (2x^2 - 4ax)\ln x + x^2$ (where $a \in \mathbb{R}$),
(I) Find the equation of the tangent line to the corresponding curve at the point $(e, f(e))$ (where $e$ is the base of the natural logarithm) when $a = 0$;
(II) Determine the monotonic intervals of the function $f(x)$.

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