
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 store offers two discount schemes: ① Buy $1$ backpack and get $1$ pen for free; ② Buy backpacks and pens at a $10\%$ discount. It is known that each backpack costs $20$ yuan and each pen costs $5$ yuan. Xiao Li and her classmates need to buy $4$ backpacks and at least $x$ pens ($x$ is no less than $4$ pens).  
$(1)$ The total cost of buying backpacks and pens according to discount scheme ① is ______ yuan, and the total cost according to discount scheme ② is ______ yuan. (Express in terms of $x$ in its simplest form)  
$(2)$ If $x=30$, by calculation, determine whether it is more cost-effective to buy according to scheme ① or scheme ②.  
$(3)$ When $x=30$, can you come up with a more cost-effective purchasing plan? Please write down your purchasing plan directly.

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