
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 company plans to purchase desk lamps and flashlights from a store. It is known that the unit price of a desk lamp is $50$ yuan higher than the unit price of a flashlight. The amount spent on purchasing desk lamps is equal to the amount spent on purchasing flashlights, which is $240$ yuan for desk lamps and $90$ yuan for flashlights.<br/>$(1)$ Find out how much it costs to purchase one desk lamp and one flashlight each?<br/>$(2)$ After negotiation, the store offers the company a promotion of giving a free flashlight for every desk lamp purchased. If the company needs a number of flashlights that is two times the number of desk lamps plus 8 more, and the total cost of purchasing desk lamps and flashlights does not exceed $2440$ yuan, then how many desk lamps can the company purchase at most?

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