
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 curve C be defined by $f(x) = x^3 - ax + b$ ($a, b \in \mathbb{R}$).

(1) If the function $g(x) = \ln x - \frac{a}{6}[f'(x) + a] - 2x$ has a decreasing interval, find the range of values for $a$ ($f'(x)$ is the derivative of $f(x)$).

(2) If a tangent line to curve C from a point A(1, 0) outside the curve exists exactly three times, find the relationship between $a$ and $b$.

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