
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 $f(x) = x^3 - x^2 - x + 2$.

(Ⅰ) Find the intervals of monotonicity and the extreme values of $f(x)$.

(Ⅱ) If it is given that for $x \in [-1, 2]$, the inequality $-3 \leq af(x) + b \leq 3$ holds, find the maximum value of $a - b$.

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