
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
(The full score for this question is 12 points) If the solution set of the inequality $(1-a)x^2-4x+6>0$ is $\{x|-3<x<1\}$.

(1) Solve the inequality $2x^2+(2-a)x-a>0$;  
(2) For what value of $b$, the solution set of $ax^2+bx+3\geq0$ is $\mathbb{R}$.

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