
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 \(m\), which also 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 \(m\). 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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