
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 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. Assume that a random point with coordinates \( (x ; y) \) is selected from the unit square \( F \). When Maria Petrovna ate half of the jam she had left, she has \( \frac{x}{2} \) liters of jam remaining. Therefore, the event \( A \) "Maria Petrovna and Olga Pavlovna together have not less than 1 liter" is written as \(\frac{x}{2}+y \geq 1\) and is represented by a triangle located above the line \( y=1-\frac{x}{2} \).

Therefore,

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

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