
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
The coefficients \( p \) and \( q \) of the quadratic equation \( x^{2}+p x+q=0 \) are chosen at random in the interval \( (0, 2) \). What is the probability that the roots of this equation will be real numbers?

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