
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 \( Q(3, -2) \) 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 \( 2x + y = 0 \), and the coordinates of \( Q'' \) are \((-1, 5)\). Determing the equation of line \( m \).
A) \( 3x + y = 0 \)
B) \( 3x - y = 0 \)
C) \( x - 3y = 0 \)
D) \( 2x - 3y = 0 \)
E) \( 2x + 3y = 0 \)

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