
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 $f(x)= \frac {1}{2}x^{3}+ax-b$, and that it is increasing in the interval $[-1,1]$, find the probability that for any two real numbers $a$ and $b$ chosen from the interval $[0,1]$, the function $f(x)$ has exactly one zero in the interval $[-1,1]$.

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