
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
Let the function $f(x) = x^3 - ax^2 + 3x + b$, where $a, b$ are real constants, and its graph has a tangent line at the point $(1, f(1))$ that is parallel to the x-axis.  
(1) Find the value of $a$;  
(2) If for any $x \in [-1, 4]$, $f(x) > f'(x)$ holds, find the range of values for $b$.

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