
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 held a promotion during the "May Day" period, and according to the total amount of one-time purchases by customers based on the marked prices of the goods, corresponding discount methods were stipulated:<br/>① If the total amount does not exceed $500, no discount will be given;<br/>② If the total amount exceeds $500 but does not exceed $800, an 20% discount will be given based on the total purchase amount;<br/>③ If the total amount exceeds $800, an 20% discount will be given on the first $800, and a 40% discount will be given on the amount exceeding $800.<br/>During the promotion period, Xiaohong and her mother each chose an item. If they pay separately, they should pay $480 and $520 respectively; if they pay together, they only need to pay a total of ____ yuan.

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