
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 $x=3$ is an extremum point of the function $f(x) = (x^2 + ax + b)e^{3-x}$, where $x \in \mathbb{R}$.

(Ⅰ) Find the relationship between $a$ and $b$ (express $b$ in terms of $a$), and determine the intervals of monotonicity for $f(x)$;

(Ⅱ) When $a > 0$, find the range of $f(x)$ on the interval $[0, 4]$.

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