
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
We have a rectangular prism, one of whose edges is five times longer than another of its edges. If we were to increase the height of the prism by $2 \mathrm{~cm}$, its volume would increase by $90 \mathrm{~cm}^{3}$. If we were then to change the height of this enlarged prism to half, the volume of the new prism would be three-fifths of the volume of the original prism.

What could be the dimensions of the original rectangular prism? Determine all possibilities.

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