
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 set $A=\{ x|1\leqslant x\leqslant 6\}$, consider the quadratic equation in $x$: $\frac{1}{4}x^{2}+\sqrt{b}x+2c=0$, where $b,c\in A$ and $b,c\in \mathbb{Z}$. Find the probability that this quadratic equation has a solution.

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