
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
In order to cultivate good reading habits among students, a certain school decided to carry out a "Love Reading, Love Sharing" recitation activity and set up first, second, and third prizes. They needed to purchase 80 prizes in total. The number of second prize items is 4 times less than the number of first prize items minus 10. The unit prices of the various prizes are as shown in the table below:

|            | First Prize | Second Prize | Third Prize |
|------------|-------------|--------------|-------------|
| Unit Price | $18         | $12          | $6          |
| Quantity   | $x          |              |             |

$(1)$ Please express the number of second prize items as an algebraic expression containing $x$ and the number of third prize items as an algebraic expression containing $x$ (simplified expressions).<br/>
$(2)$ Please express the total cost of purchasing 80 prizes as an algebraic expression containing $x$ (simplified result).<br/>
$(3)$ If 12 first prize items are purchased, how much money in total did the school spend on purchasing these 80 prizes?

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