
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 shopping mall is selling two types of goods, A and B, and is running a promotional event with the following scheme:

| Activity | A (Price) | B (Price)  |
|---|---|---|
| Original Price | 90  |  100 |
| Cashback for each item  | 30% of the original price  | 15% of the original price  |

For example, buying one piece of A costs: $90 (1 - 30%)$

For the second promotional activity, if the total number of goods purchased exceeds 100 pieces (the combination of different goods is allowed), then cashback will be 20% of the original price.

1. If a customer purchases 30 pieces of A and 90 pieces of B, which promotional scheme is more cost-effective? How much money can they save?
2. If a customer purchases $x$ pieces of A (where $x$ is an integer), and the number of pieces of B purchased is more than twice that of A by one piece, which promotional scheme should the customer choose to maximize their savings? Explain the reasoning.

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