
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 celebrate the successful convening of the two sessions, a certain middle school held a knowledge competition with the theme of "two sessions." It was decided to purchase pens and mechanical pencils of the same brand as prizes for the winning students. After checking the prices at the stationery store, it was found that 2 pens and 5 mechanical pencils of the brand cost a total of 75 yuan, and 3 pens and 2 mechanical pencils cost a total of 85 yuan.  
$(1)$ Find the price of each pen and mechanical pencil of this brand.  
$(2)$ After negotiation, the stationery store offered a promotion that for every pen purchased, a mechanical pencil of the same brand would be given for free. If the school needs a number of mechanical pencils that is 2 times the number of pens plus 8 more pencils, and the total cost of purchasing pens and mechanical pencils is less than 670 yuan, then how many pens of this brand can the school purchase at most?

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