
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 $f(x) = x^3 - (a + 1)x^2 + 3ax + 1$.

(1) If the function $f(x)$ is monotonically decreasing in the interval $(1,4)$, find the range of values for $a$.

(2) If the function $f(x)$ has a local minimum of 1 at $x = a$, find the value of $a$, and describe the monotonicity of the function $f(x)$ in the interval $(1,4)$.

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