
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
Adam has two cuboids with volumes $12 \mathrm{~cm}^{3}$ and $30 \mathrm{~cm}^{3}$, with the dimensions of each being different whole numbers in centimeters. Adam discovered that the cuboids can be glued together so that the glued faces coincide, forming a new cuboid.

What dimensions could the new cuboid have? Determine all the possibilities.

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