
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 $x_1,x_2,\ldots,x_7$ are real numbers such that
\[\begin{aligned} 
x_1+3x_2+5x_3+7x_4+9x_5+11x_6+13x_7 &= 0, \\ 
3x_1+5x_2+7x_3+9x_4+11x_5+13x_6+15x_7 &= 10, \\
5x_1+7x_2+9x_3+11x_4+13x_5+15x_6+17x_7 &= 104.
\end{aligned}\]
Find the value of $7x_1+9x_2+11x_3+13x_4+15x_5+17x_6+19x_7$.

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