
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. This corresponds to choosing a random point with coordinates \((x, y)\) from the unit square \( F \). When Maria Petrovna has eaten half of her remaining jam, she has \(\frac{x}{2}\) liters left. Therefore, the event \( A \) "together, Olga Pavlovna and Maria Petrovna have at least 1 liter" is described by the inequality \(\frac{x}{2} + y \geq 1\) and is represented by the triangle located above the line \( y = 1 - \frac{x}{2} \).

Then,
\[
\mathrm{P}(A) = \frac{S_A}{S_F} = \frac{1}{4} = 0.25
\]

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