
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 plans to send a high jump athlete to participate in an inter-school competition. They conducted 8 high jump selection competitions for two students, A and B. Their original scores (unit: cm) are as follows:

| Student/Score/Times | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th |
|---------------------|-----|-----|-----|-----|-----|-----|-----|-----|
| A                   | 169 | 165 | 168 | 169 | 172 | 173 | 169 | 167 |
| B                   | 161 | 174 | 172 | 162 | 163 | 172 | 172 | 176 |

The analysis of the 8 high jump scores for the two students is shown in the table below:

| Student/Score/Name | Mean (unit: cm) | Median (unit: cm) | Mode (unit: cm) | Variance (unit: cm^2) |
|--------------------|-----------------|-------------------|-----------------|-----------------------|
| A                  | a               | b                 | c               | 5.75                  |
| B                  | 169             | 172               | 172             | 31.25                 |

Answer the following questions based on the information provided in the tables:
1. Write down the values of a, b, and c directly from the table.
2. Among these two students, whose scores are more stable?
3. If predicting a high jump of 165 cm may win the championship, which student should the school choose to participate in the competition in order to win the championship? If predicting a high jump of 170 cm is required to win the championship, which student should the school choose to participate in the competition to win the championship? Explain your reasoning.

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