
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 first reflected about line \(m\), then the resulting point \(Q'\) is reflected about line \(\ell\) to point \(Q''\). The equation of line \(\ell\) is \(2x - 5y = 0\), and the coordinates of \(Q''\) are \((-2, 3)\). Find the equation of line \(m\).

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