
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
In an opaque bag, there are three balls, each labeled with the numbers $-1$, $0$, and $\frac{1}{3}$, respectively. These balls are identical except for the numbers on them. Now, a ball is randomly drawn from the bag, and the number on it is denoted as $m$. After putting the ball back and mixing them, another ball is drawn, and the number on it is denoted as $n$. The probability that the quadratic function $y=x^{2}+mx+n$ does not pass through the fourth quadrant is ______.

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