
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 shopkeeper wants to sell his existing stock of a popular item at one and a half times its current price. To achieve this, he plans to implement a phased price increase. He starts with a certain price increase, and when two-thirds of the stock has been sold, he raises the price again by the same percentage. This new price remains in effect until the entire stock is sold. What percentage price increases are needed to achieve the desired goal?

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