
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 $ABC$ has vertices with coordinates $A(3,4),$ $B(8,9),$ and $C(-3,7)$. After a transformation, the image points are $A'(-2,-6),$ $B'(-7,-11),$ and $C'(2,-9)$. Determine the operation performed, and if it includes reflection, find the equation of the line of reflection.

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