
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 \( f(x) = -x^3 + ax^2 + bx + c \) (where \( a, b, c \in \mathbf{R} \)) is monotonically decreasing on \( (-\infty, 0) \), monotonically increasing on \( (0,1) \), and \( f(x) \) has three zeros in \( \mathbf{R} \), one of which is 1:

(1) Find the range of values for \( f(2) \);

(2) Discuss the number of intersection points between the line \( l: y = x - 1 \) and the curve \( C: y = f(x) \).

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