
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
During the "Double Eleven" period, a supermarket promotion stipulates the following: if a consumer's cumulative purchase does not exceed $200, they will pay the original price. For customers whose cumulative purchase exceeds $200, the following discounts will be applied:<br/>

| Cumulative Purchase Amount | Discount Method |
|-----------------------------|-----------------|
| Over $200 but not exceeding $600 | The amount exceeding $200 but not exceeding $600 will be discounted by 20%. |
| Over $600 | For every $300 spent, $100 will be deducted. The amount not reaching $300 will not be discounted. For example: if the cumulative purchase amount is $658, the actual payment will be $458; if the cumulative purchase amount is $908, the actual payment will be $608. |

$(1)$ Xiao Mu's mother made a cumulative purchase of $196, she actually needs to pay ______ yuan.<br/>
$(2)$ Xiao Liang's mother made a cumulative purchase of $260, she actually needs to pay ______ yuan.<br/>
$(3)$ Xiao Mei's mother made a cumulative purchase of $x$ yuan $(200 < x \leq 600)$, then she actually needs to pay ______ yuan. (Express using an expression containing $x$).<br/>
$(4)$ Xiao Xi's mother made a cumulative purchase of $m$ yuan $(0 < m < 200)$, Xiao Bo's mother made a cumulative purchase of $(m+300)$ yuan. When checking out, Xiao Bo's mother paid $250$ yuan more than Xiao Xi's mother. Find the value of $m$.<br/>
$(5)$ Xiao Bei and his mother bought the following items at the supermarket: a rice cooker for $445, five pounds of pork at $38 per pound, two bottles of milk at $75 per bottle, two trays of eggs at $35 per tray, a pack of tissues for $27, a stationery bag for $16. The mother is ready to make a one-time payment. Xiao Bei stops his mother, saying that if he goes to get a $2 pen before making the payment, they will save ______ yuan compared to making the payment now.

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