
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 $f(x) = \frac {1}{3}x^{3}+ax^{2}+b^{2}x+1$, where \( a \) is chosen from the numbers {1, 2, 3} and \( b \) is chosen from the numbers {0, 1, 2}, what is the probability that the function has two distinct extreme points?

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