
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 
\[
\renewcommand{\arraystretch}{1.5} 
\begin{pmatrix} 
\frac{3}{25} & \frac{4}{25} & -\frac{2}{5} \\ 
\frac{4}{25} & \frac{7}{25} & \frac{1}{5} \\ 
-\frac{2}{5} & \frac{1}{5} & \frac{15}{25} 
\end{pmatrix} 
\renewcommand{\arraystretch}{1}
\]
find the direction vector of line $\ell$ that passes through the origin. Enter your answer in the form $\begin{pmatrix} a \\ b \\ c \end{pmatrix}$, where $a, b, c$ are integers, $a > 0$, and $\gcd(|a|,|b|,|c|) = 1$.

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