
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

The cake is packed in a box with a square base. The height of the box is half the length of a side of this square. A ribbon of 156 cm in length is sufficient to tie the box and make a bow on top (as shown in the left picture). To tie it with the same kind of bow on the side (as shown in the right picture), a ribbon of 178 cm in length is needed. Find the dimensions of the box.

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