
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
There are five opaque cards with the numbers $-2$, $0$, $1$, $2$, and $3$ respectively on the front. Other than the numbers, all the cards are identical. Now, with the back of the cards facing up, they are shuffled and one card is randomly drawn. Let the number on the card be denoted as $a$. The probability that the number $a$ drawn satisfies the conditions that the hyperbola $y=\frac{a-2}{x}$ is in the second and fourth quadrants, and that the parabola $y=ax^{2}+2x-3$ intersects the $x$-axis is ____.

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