
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 shop offers an initial discount of $25\%$ on all items. A week later, an additional discount of $15\%$ is applied to the already discounted prices. Finally, an extra $10\%$ discount is applied to the new sale price on a special sale day. The shop advertises that the cumulative discount equals $50\%$ off the original prices. Compute the actual total discount and find the percentage difference between the shop's claim and the true discount.

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