
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 certain rectangle had its dimensions expressed in whole numbers of decimeters. Then, it changed its dimensions three times. First, one of its dimensions was doubled and the other was adjusted so that the area remained the same. Then, one dimension was increased by $1 \mathrm{dm}$ and the other decreased by $4 \mathrm{dm}$, keeping the area the same. Finally, its shorter dimension was reduced by $1 \mathrm{dm}$, while the longer dimension remained unchanged.

Determine the ratio of the lengths of the sides of the final rectangle.

(E. Novotná)

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