
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 $y_1, y_2, ... , y_8$ are real numbers such that
\[
\begin{aligned}
y_1 + 4y_2 + 9y_3 + 16y_4 + 25y_5 + 36y_6 + 49y_7 + 64y_8 &= 3, \\
4y_1 + 9y_2 + 16y_3 + 25y_4 + 36y_5 + 49y_6 + 64y_7 + 81y_8 &= 15, \\
9y_1 + 16y_2 + 25y_3 + 36y_4 + 49y_5 + 64y_6 + 81y_7 + 100y_8 &= 140.
\end{aligned}
\]
Find the value of $16y_1 + 25y_2 + 36y_3 + 49y_4 + 64y_5 + 81y_6 + 100y_7 + 121y_8$.

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