
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 that $a \in \mathbb{R}$, if the solution set of the inequality $(1-a)x^2 - 4x + 6 > 0$ is $(-3, 1)$,
(1) Solve the inequality $2x^2 + (2 - a)x - a > 0$;
(2) If the solution set of the inequality $ax^2 + bx + 3 \geq 0$ is $\mathbb{R}$, find the range of values for the real number $b$.

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