
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
Let $f(x) = (x - a)^2\ln{x}$, where $a \in \mathbb{R}$.
(Ⅰ) If $x = e$ is an extremal point of $y = f(x)$, find the value of the real number $a$;
(Ⅱ) Determine the range of the real number $a$ such that for any $x \in (0, 3e]$, it always holds that $f(x) \leq 4e^2$.
Note: $e$ is the base of the natural logarithm.

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