
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
Given the matrix for reflecting over a certain line $\ell$, passing through the origin:
\[
\begin{pmatrix}
\frac{8}{17} & -\frac{15}{17} \\
-\frac{15}{17} & -\frac{8}{17}
\end{pmatrix}.
\]
Find the direction vector of line $\ell$. The answer should be in the form $\begin{pmatrix} x \\ y \end{pmatrix}$, where $x$ and $y$ are integers, $x > 0$, and $\gcd(|x|,|y|) = 1$.

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