
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 constructed a cuboid using $1 \mathrm{~cm}$ edge cubes. If we were to remove one column from the cuboid, the remaining structure would consist of 602 cubes. If, instead, we removed one row from the top layer, the remaining structure would have 605 cubes. What are the dimensions of the cuboid?

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