
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 store offers a discount of 40% on a collection of bags. A second promotional event applies an additional 10% off the already discounted prices. The store advertises that the total discount on these items is 50%. What is the difference between the actual discount and the store's claimed discount, as a percentage of the original price?

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