
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
Triangle $DEF$ has vertices with coordinates $D(1,2),$ $E(6,7),$ and $F(-5,5)$. The triangle is reflected about line $M$. The image points are $D'(1,-4),$ $E'(6,-9),$ and $F'(-5,-7)$. What is the equation of line $M$?

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