
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
Solve the application problems by setting up equations.  
(1) A certain number of candies are distributed to some children. If each child gets 3 candies, there are 12 candies left; if each child gets 5 candies, there are 10 candies short. How many children are there?  
(2) Xiao Ming went to a stationery store to buy 2B pencils. The shopkeeper said, "If you buy more, I'll give you a 20% discount." Xiao Ming calculated that if he bought 50 pencils, he would save 6 yuan compared to buying at the original price. What is the original price of each pencil?

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