
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
The "Strawberry Music Festival" organizing committee has set up three types of tickets: A, B, and C. Class 1 of Grade 2 bought 3 tickets of type A, 7 tickets of type B, and 10 tickets of type C. The class leader randomly selects the audience list from all classmates, and each student has only one chance. It is known that there are 50 students in the class. Please solve the following problems based on the question:<br/>$(1)$ What is the probability that a student from this class can attend the "music festival" event?<br/>$(2)$ The students strongly demand more type A tickets, and require the probability of each person drawing a type A ticket to reach $20\%$. How many more type A tickets need to be purchased?

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