
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
Solve the quadratic equation $Ax^2+Bx+C=0$ under the following conditions:
(1) If $A=1$, and $B$ and $C$ are the outcomes from rolling a die twice, calculate the probability that the equation has real roots.
(2) Given that $B=-A$ and $C=A-3$, with $A$ being a random real number such that the equation has real roots, find the probability that the equation has at least one non-negative real root.

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