
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 $x_1, x_2, \ldots, x_6$ are real numbers such that
\[
x_1 + 3x_2 + 5x_3 + 7x_4 + 9x_5 + 11x_6 = 2, \\
3x_1 + 5x_2 + 7x_3 + 9x_4 + 11x_5 + 13x_6 = 15, \\
5x_1 + 7x_2 + 9x_3 + 11x_4 + 13x_5 + 15x_6 = 52.
\]
Find the value of $7x_1 + 9x_2 + 11x_3 + 13x_4 + 15x_5 + 17x_6$.

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