
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 type of juvenile book, if sold at its original price, yields a profit of 0.24 yuan per book. Now, selling it at a reduced price has doubled the sales volume and increased the total profit by 0.5 times. How much has the price per book been reduced?

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