
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 a function $f(x) = dx^3 + cx^2 + bx + a$, satisfying $f'(x) = -3x^2 + 3$.

(1) Find the values of the real numbers $d$, $c$, and $b$;  
(2) Find the extreme values of the function $f(x)$;  
(3) For what value of the real number $a$ does the function $f(x)$ have only two intersections with the x-axis.

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