
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 parabola defined by the equation \(y=(x-3)^2+4\). The graph of this parabola is:
1. Rotated 180 degrees about its vertex.
2. Shifted 4 units to the right.
3. Shifted 3 units down.
Find the sum of the x-coordinates where the parabola intersects the x-axis.

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