
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 \( Q(-2, 3) \) 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 \( 3x + 4y = 0 \), and the coordinates of \( Q'' \) are \((3, -2)\). What is the equation of line \( m \)?
- **A)** \( 7x + 25y = 0 \)
- **B)** \( 7x - 25y = 0 \)
- **C)** \( 3x - 4y = 0 \)
- **D)** \( 25x + 7y = 0 \)

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