
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
To enhance students' reading abilities, our school's first-year class purchased two books, "Morning Blossoms and Evening Blossoms" and "Journey to the West," at costs of $14,000 and $7,000, respectively. It is known that the unit price of "Morning Blossoms and Evening Blossoms" is 1.4 times the unit price of "Journey to the West," and the quantity of "Morning Blossoms and Evening Blossoms" ordered is 300 more than the quantity of "Journey to the West" ordered.
$(1)$ Find the unit prices of the two books ordered by our school's first-year class.
$(2)$ A certain class in our first-year level plans to order an additional 10 books of these two types for backup, with the condition that the quantity of "Morning Blossoms and Evening Blossoms" ordered is not less than 3, and the total cost does not exceed $124. How many possible ordering schemes are there for this class, and what is the lowest total cost according to these schemes?

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