
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 $-2$, $-1$, $0$, $1$, and $2$ respectively on their fronts, and all other aspects of the cards are the same. Now, the cards are placed face down, shuffled, and one card is randomly chosen. Let the number on the chosen card be denoted as $a$, and let $b$ be the result of adding $1$ to that number. The probability that the one-variable quadratic equation $ax^{2}+bx+\frac{a}{4}=0$ has a solution is ______.

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