
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
$$q(x,y) = b_0 + b_1x + b_2y + b_3x^2 + b_4xy + b_5y^2 + b_6x^3 + b_7x^2y + b_8xy^2 + b_9y^3.$$
Suppose that
\begin{align*}
q(0,0) &= q(1,0) = q(-1,0) = q(0,1) = q(0, -1) = q(1,1) = q(1, -1) = q(-1,1) = q(-1,-1) = 0.
\end{align*}
Find a point $(r,s)$ where $q(r,s) = 0$ and neither $r$ nor $s$ are integers.

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