
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
A certain school needs to select one student from two students, A and B, to participate in the national high school mathematics competition. The recent results of 5 mock exams for the two students are as follows:

|         | 1st   | 2nd   | 3rd   | 4th   | 5th   |
|---------|-------|-------|-------|-------|-------|
| A's score | 78    | 80    | 65    | 85    | 92    |
| B's score | 75    | 86    | 70    | 95    | 74    |

$(1)$ Based on the exam results of the last 5 times for A and B, who do you think is more suitable to participate? Please explain your reasoning.

$(2)$ If the recommendation for participating in the national high school mathematics competition is as follows:

Plan 1: Each person randomly selects 1 question from 5 optional questions. If answered correctly, they can participate in the national high school mathematics competition, otherwise they are eliminated.

Plan 2: Each person randomly selects 3 questions from 5 optional questions. If they answer at least 2 questions correctly, they can participate in the national high school mathematics competition, otherwise they are eliminated.

It is known that student A only knows how to solve 3 of the 5 optional questions. In this case, which answer plan should student A choose to have a higher chance of participating in the national high school mathematics competition? Please explain your reasoning.

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