
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 parabolas \( y = (x - 2)^2 \) and \( x + 7 = (y + 2)^2 \) intersect at points \( (x_1, y_1), (x_2, y_2), (x_3, y_3), \) and \( (x_4, y_4) \). Calculate the sum
\[ x_1 + x_2 + x_3 + x_4 + y_1 + y_2 + y_3 + y_4. \]

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