
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 $f(x) = x^2 - (a+b)x + 3a$,
1. If the solution set of the inequality $f(x) \leq 0$ is $[1, 3]$, find the values of the real numbers $a$ and $b$.
2. If $b = 3$, find the solution set of the inequality $f(x) > 0$.

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