
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 for which the product of $540$ and $x$ is a square and the product of $540$ and $y$ is a cube. What is the sum of $x$ and $y$?
A) 50
B) 55
C) 65
D) 75
E) 90

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