
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
Guandu Babao is a famous specialty snack in Guandu District. Due to its unique production process, Guandu Babao has a crispy and sweet skin, which is both soft and chewy. In 2009, Guandu Babao was included in the second batch of intangible cultural heritage protection list in Kunming. Thanks to the developed online sales model, this pastry gradually spread beyond Kunming and sold well nationwide. A certain Taobao wholesale store found through market research (selling in whole boxes): ① If the profit per box of Guandu Babao is $50, they can sell 500 boxes in a month; ② Without considering other factors, if the price per box is reduced by $1, they can sell 20 more boxes. To seize the business opportunities during the National Day holiday, the online store decided to offer discounts, setting the price reduction per box to be $x.

$(1)$ If the total profit from selling Guandu Babao in October this year is $28000, how much should the online store reduce the price per box in October?

$(2)$ Under the same conditions as above, can the total profit in November reach $30000? Please explain through calculations.

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