
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
Suppose that Maria Petrovna has \( x \) liters of jam left, and Olga Pavlovna has \( y \) liters of jam left. The values \( x \) and \( y \) are chosen randomly and independently from the interval from 0 to 1. This can be thought of as selecting a random point with coordinates \( (x, y) \) from a unit square \( F \). When Maria Petrovna eats half of her remaining jam, she has \( \frac{x}{2} \) liters left. Therefore, the event \( A \) "Maria Petrovna and Olga Pavlovna have together not less than 1 liter of jam" can be expressed by the inequality \( \frac{x}{2} + y \geq 1 \), which corresponds to the area above the line \( y = 1 - \frac{x}{2} \).

Then the probability of event \( A \) is:

\[
\mathrm{P}(A) = \frac{S_{A}}{S_{F}} = \frac{1}{4} = 0.25
\]

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