
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 for this question is 12 points.)

Given the function $f(x) = -x^3 + x^2 + ax + b$ ($a, b \in \mathbb{R}$).

(1) If $a = 3$, determine the intervals of monotonicity for the function $f(x)$.

(2) If the slope of the tangent line at any point $(x_0, f(x_0))$ on the graph of the function $f(x)$ is less than $2a^2$, find the range of values for $a$.

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