
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
Determine the values of a and b such that the function \( f(x) = \frac{x^4 + ax^2 + b}{x^2 - 4} \) is continuous at \(x = 2\) and \(x = -2\).
**A)** \( a = 0, b = -16 \)  
**B)** \( a = 1, b = -20 \)  
**C)** \( a = -1, b = -12 \)  
**D)** \( a = 2, b = -24 \)  
**E)** \( a = -2, b = -8 \)

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