
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
Assume that $x_1, x_2, \ldots, x_8$ are real numbers such that
\[\begin{aligned} 
x_1 + 5x_2 + 10x_3 + 17x_4 + 26x_5 + 37x_6 + 50x_7 + 65x_8 &= 2, \\
5x_1 + 10x_2 + 17x_3 + 26x_4 + 37x_5 + 50x_6 + 65x_7 + 82x_8 &= 14, \\
10x_1 + 17x_2 + 26x_3 + 37x_4 + 50x_5 + 65x_6 + 82x_7 + 101x_8 &= 140.
\end{aligned}\]
Find the value of $17x_1 + 26x_2 + 37x_3 + 50x_4 + 65x_5 + 82x_6 + 101x_7 + 122x_8$.

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