
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
Determine the direction vector of line $m$ which passes through the origin and is associated with the reflection matrix
\[
\begin{pmatrix} 
\frac{3}{5} & \frac{4}{5} \\ 
\frac{4}{5} & -\frac{3}{5} 
\end{pmatrix}.
\]
Find the direction vector of line $m$ 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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