
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 $f(x) = 2x^3 - 3(a+1)x^2 + 6ax + 8$, where $a\in \mathbb{R}$.

(1) If $f'(3) = 0$, find the value of the constant $a$;

(2) If $f(x)$ is increasing on the interval $(-\infty, 0)$, determine the range of $a$.

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