
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 the function $f(x) = 2x^3 - 3(a+1)x^2 + 6ax$, where $a \in \mathbb{R}$.

(Ⅰ) Discuss the number of zeros of the derivative $f'(x)$ of $f(x)$ on the interval $[-1, 3]$.

(Ⅱ) If for any $a \in [-3, 0]$, and any $x_1, x_2 \in [0, 2]$, the inequality $m - am^2 \geq |f(x_1) - f(x_2)|$ always holds, find the range of the real number $m$.

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