
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
Given $r$ as the resulting number when both the base and the exponent of $a^b$ are doubled, if $r$ equals the product of $a^{2b}$ and $y^{2b}$, where all variables are positive, determine the value of $y$.
A) $1$  
B) $2$  
C) $4^{b}$  
D) $2^{2b}$  
E) $a^{b}$

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