
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
The graph of the parabola defined by $y = (x-3)^2 + 4$ is rotated 180 degrees about its vertex, then shifted 4 units to the right, and then shifted 3 units down. The resulting parabola has zeros at $x=p$ and $x=q$. What is $p+q$?

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