
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
The matrix for reflecting over a certain line $\ell,$ which passes through the origin, is given by
\[\begin{pmatrix} \frac{3}{5} & -\frac{4}{5} \\ -\frac{4}{5} & -\frac{3}{5} \end{pmatrix}.\]Find the direction vector of line $\ell.$  Enter your answer in the form $\begin{pmatrix} a \\ b \end{pmatrix},$ where $a,$ and $b$ are integers, $a > 0,$ and $\gcd(|a|,|b|) = 1.$

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