
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
The real numbers \( x_1, x_2, x_3, x_4 \) are such that

\[
\begin{cases}
x_1 + x_2 \geq 12 \\
x_1 + x_3 \geq 13 \\
x_1 + x_4 \geq 14 \\
x_3 + x_4 \geq 22 \\
x_2 + x_3 \geq 23 \\
x_2 + x_4 \geq 24 \\
\end{cases}
\]

What is the minimum value that the sum \( x_1 + x_2 + x_3 + x_4 \) can take?

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