
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
(The full score of this question is 12 points) Given the function $f(x) = x^3 - 3ax^2 - bx$, where $a, b$ are real numbers.  
(1) If $f(x)$ takes an extreme value of 2 at $x = 1$, find the values of $a$ and $b$;  
(2) If $f(x)$ is a decreasing function on the interval $[-1, 2]$ and $b = 9a$, find the range of values for $a$.

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