
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 item cost 64 rubles. Each month, its price changed by 50% either increasing or decreasing. It is known that over six months, the price increased three times and decreased three times (the order of these changes is unknown). Can the price of the item be determined after six months? If yes, what did it become?

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