
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
A very large sphere has a volume of $450\pi$ cubic units. A smaller sphere has a volume that is $8\%$ of the volume of the larger sphere, and another medium sphere has a volume that is $27\%$ of the volume of the larger sphere. What are the ratios of the radii of the smaller to the larger sphere and the medium to the larger sphere? Express your answer as common fractions.

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