
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:
\[\begin{aligned} 
x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7 &= 1, \\
4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7 &= 8, \\
9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7 &= 81. 
\end{aligned}\]
Find the value of $25x_1+36x_2+49x_3+64x_4+81x_5+100x_6+121x_7$.

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