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

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