
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 that results when the base of $a^b$ is quadrupled and the exponent is tripled, where $a, b > 0$. If $r$ equals the product of $a^b$ and $x^b$ where $x > 0$, then find $x$ in terms of $a$ and $b.$
A) $16 a^2$  
B) $27 a^2$  
C) $64 a^2$  
D) $48 a^2$

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