
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 $420$ and $x$ is a square and the product of $420$ and $y$ is a cube. Determine the sum of $x$ and $y$.
A) 2115
B) 22155
C) 11078
D) 22050

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