
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
Malvina and Buratino play by the following rules: Malvina writes six different numbers in a row on the board, and Buratino invents his own four numbers \( x_1, x_2, x_3, x_4 \). He then writes under each number of Malvina any of the sums \( x_1 + x_2, x_1 + x_3, x_1 + x_4, x_2 + x_3, x_2 + x_4, x_3 + x_4 \) (each sum only once). Buratino gets 3 apples for each sum that equals the number above it and 1 apple for each sum that is greater than the number above it. What is the maximum number of apples Buratino can be guaranteed to receive?

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