
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
Harry and Sandy want to meet at a point in Hogwarts that is the midpoint of their coordinates. Harry is standing at \((12, 3)\), and Sandy is standing at \((4, 9)\). However, they want to ensure that the point they choose to meet does not fall on the line defined by the equation \(y = -x + 6\). At what coordinate will they meet, and is this coordinate on the line?

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