
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 positive integers \(x\) and \(y\) are the two smallest positive integers such that the product of \(450\) and \(x\) is a square, and the product of \(450\) and \(y\) is a cube. What is the sum of \(x\) and \(y\)?
A) 48  
B) 58  
C) 62  
D) 82  
E) 100

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