
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 \( x_1, x_2, \ldots, x_7 \) are real numbers such that
\[
\begin{aligned}
x_1 + 9x_2 + 25x_3 + 49x_4 + 81x_5 + 121x_6 + 169x_7 &= 2, \\
9x_1 + 25x_2 + 49x_3 + 81x_4 + 121x_5 + 169x_6 + 225x_7 &= 24, \\
25x_1 + 49x_2 + 81x_3 + 121x_4 + 169x_5 + 225x_6 + 289x_7 &= 246.
\end{aligned}
\]
Find the value of \( 49x_1 + 81x_2 + 121x_3 + 169x_4 + 225x_5 + 289x_6 + 361x_7 \).

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