
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

If \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\) satisfy the following system of equations:
\[
\begin{cases}
2x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 6, \\
x_{1} + 2x_{2} + x_{3} + x_{4} + x_{5} = 12, \\
x_{1} + x_{2} + 2x_{3} + x_{4} + x_{5} = 24, \\
x_{1} + x_{2} + x_{3} + 2x_{4} + x_{5} = 48, \\
x_{1} + x_{2} + x_{3} + x_{4} + 2x_{5} = 96,
\end{cases}
\]
find the value of \(3x_{4} + 2x_{5}\).

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