
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 brand of soap originally sells for 2 yuan per piece. For purchases of more than 2 pieces, the store offers two promotional sales methods. The first method: one piece of soap is sold at the original price, and the rest are sold at 70% of the original price; the second method: all are sold at 80% of the original price. Find the minimum quantity of soap that needs to be purchased to make the discount received from the first method greater than that from the second method when purchasing the same quantity of soap.

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