
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
There is a sheet of metal in the shape of a rectangle, where the ratio of length to width is $2:1$. An open-top box is made from this sheet by cutting squares with sides of 3 cm from each corner and folding up the sides. Determine the dimensions of the metal sheet if the volume of the box is $168 \mathrm{~cm}^{3}$.

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