
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 the function $f(x) = kx^3 - 3x^2 + 3$  
(1) When $k=0$, find the area of the enclosed shape formed by the graph of function $f(x)$ and the line $y=x-1$;  
(2) When $k>0$, find the intervals of monotonicity for the function $f(x)$.

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