
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
Distinct lines $\ell$ and $m$ lie in the $xy$-plane. They intersect at the origin. Point $Q(-2, 5)$ is reflected about line $\ell$ to point $Q'$, and then $Q'$ is reflected about line $m$ to point $Q''$. The equation of line $\ell$ is $3x - y = 0$, and the coordinates of $Q''$ are $(5,2)$. What is the equation of line $m$?
A) x + 2y = 0
B) x – 2y = 0
C) 2x + y = 0
D) 2x - y = 0

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