
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 vegetable vendor purchased cucumbers and potatoes from the vegetable wholesale market for a total of $114$ yuan, and brought a total of $40kg$ of vegetables to the market. The wholesale and retail prices of cucumbers and potatoes on that day are shown in the table below:

| Item   | Wholesale Price (yuan/kg) | Retail Price (yuan/kg) |
|--------|---------------------------|------------------------|
| Cucumber | $3$                     | $5$                    |
| Potato   | $2.4$                   | $4$                    |

$(1)$ How many kilograms of cucumbers and potatoes did the vendor purchase that day?  
$(2)$ If all the cucumbers and potatoes are sold out, how much money will the vendor earn?

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