
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 the function $f(x) = -3x^2 + a(5-a)x + b$, where $a, b \in \mathbb{R}$.

(1) If the solution set of the inequality $f(x) > 0$ is $(-1, 3)$, find the values of the real numbers $a$ and $b$;  
(2) If $b$ is a constant, solve the inequality about $a$ for $f(1) < 0$.

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