
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 the eve of the sports meeting, Guangming Middle School will purchase basketballs and soccer balls as prizes. If buying 6 basketballs and 8 soccer balls costs a total of 1700 yuan, and buying one basketball costs 50 yuan more than buying one soccer ball.

(1) Find the price of one basketball and one soccer ball.

(2) This year, the school plans to purchase a total of 10 of these basketballs and soccer balls. Coincidentally, the mall is having a promotion where basketballs are discounted by 10% and soccer balls are discounted by 15%. If the total cost of buying these two types of balls does not exceed 1150 yuan, how many basketballs can be purchased at most?

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