
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
Let \((x_1, y_1), (x_2, y_2),\) and \((x_3, y_3)\) be three different real solutions to the system of equations:
\[
\begin{cases}
x^3 - 5xy^2 = 21 \\
y^3 - 5x^2y = 28
\end{cases}
\]
Find the value of \(\left(11 - \frac{x_1}{y_1}\right)\left(11 - \frac{x_2}{y_2}\right)\left(11 - \frac{x_3}{y_3}\right)\).

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