
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
The new science textbook will have a cover price of $\$30$. The local bookstore is offering two discounts—a $\$5.00$ discount and a $10\%$ discount—and an additional $\$2.00$ discount if the total after the first two discounts is over $\$20$. In what sequence should the shopper apply these discounts to minimize their final cost, and how much cheaper is this sequence compared to the alternative?

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