
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
Assume that Maria Petrovna has \( x \) liters and Olga Pavlovna has \( y \) liters of jam left. The numbers \( x \) and \( y \) are randomly and independently chosen from the interval from 0 to 1. Consider a random point with coordinates \( (x, y) \) from the unit square \( F \). When Maria Petrovna ate half of her remaining jam, she had \( \frac{x}{2} \) liters left. Therefore, the event \( A \) "Olga Pavlovna and Maria Petrovna together have at least 1 liter" is described by the inequality \( \frac{x}{2} + y \geq 1 \) and is represented by the region above the line \( y = 1 - \frac{x}{2} \).

Given this setup, calculate the probability \( \mathrm{P}(A) \).

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