
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
Consider the points $P(1, 2)$, $Q(4, 6)$, and $R(7, 2)$ arranged in the coordinate system to form a shape $\Delta PQR$. This shape is first rotated 180 degrees around the point $P$ and then translated three units to the right and four units downward. What is the midpoint of segment $Q'R'$ after these transformations?

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