
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
Teacher Li led students to visit the science museum. The number of students is a multiple of 5. According to the regulations, teachers and students pay half the ticket price, and each person's ticket price happens to be an integer. The total payment was 1599 yuan. 

(1) How many students are in the class?
(2) What is the stipulated ticket price per person?

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