
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 \( y = x^2 - 5x + 9 \) is rotated 180 degrees around the origin. What is the equation of the new parabola?

(a) \( y = x^2 + 5x + 9 \)  
(b) \( y = x^2 - 5x - 9 \)  
(c) \( y = -x^2 + 5x - 9 \)  
(d) \( y = -x^2 - 5x + 9 \)  
(e) \( y = -x^2 - 5x - 9 \)

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