
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 couch cost 62,500 rubles. Its price was adjusted by 20% each month, either increasing or decreasing. Over six months, the price increased three times and decreased three times (the order of these changes is unknown). Can you uniquely determine the price of the couch after six months? If so, what was its price?

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