
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 $f(x) = x - x^3e^{ax+b}$. The tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ is $y = -x + 1$.  
$(Ⅰ)$ Find the values of $a$ and $b$.  
$(Ⅱ)$ Let $g(x) = f'(x)$. Find the intervals where $g(x)$ is monotonic.  
$(Ⅲ)$ Find the number of extreme points of $f(x)$.

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