
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 "Double Eleven". According to the total amount of one-time shopping 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 amount exceeds $500 but does not exceed $800, an 20% discount will be given based on the total amount;<br/>③ If the amount exceeds $800, an 20% discount will be given on the first $800 and a 40% discount will be given on the amount exceeding $800.<br/>$(1)$ During the promotion, Xiaohong found two items she liked. If purchased separately, she would need to pay $480$ yuan and $520$ yuan respectively; if purchased together, she would only need to pay a total of ______ yuan.<br/>$(2)$ During the promotion, the marked price of a certain item selected by Xiaohong is $a$ yuan $\left(a \gt 800\right)$, then she should pay ______ yuan.<br/>$(3)$ During the promotion, if Xiaohong has purchased two items, $A$ and $B$, successively in the mall and found that the total marked price of the two items is $2000$ yuan $(B$ item has a higher amount), and the total marked price of item $A$ is $x$ yuan, find out how much money Xiaohong paid in total for the two purchases?

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