
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
Let \( r \) be the number obtained when both the base and the exponent of \( a^b \) are quadrupled, where \( a, b > 0 \). If \( r \) equals the product of \( a^b \) and \( y \) where \( y = x^2 \) and \( x > 0 \), then find \( x \).
A) \( 16a^{1.5b} \)
B) \( 16^b a^{1.5b} \)
C) \( 256a^{3b} \)
D) \( 16^b a^{2b} \)
E) \( 16a^{2b} \)

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