
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 dance team at a certain school has 16 students. The heights of all students were measured and recorded as follows:
- Heights of 16 students: 161, 162, 162, 164, 165, 165, 165, 166, 166, 167, 168, 168, 170, 172, 172, 175.
- Average, median, and mode of the heights of the 16 students:
| Average | Median | Mode |
|---------|--------|------|
| 166.75  |   m    |  n   |

(1) Write down the values of m and n.
(2) For different groups of students, if a group has a smaller variance in heights, it is considered to have a better stage performance. Based on this inference, in the following two groups of students, the group with a better stage performance is ______ (Fill in "Group A" or "Group B"):
| Group A heights | 162 | 165 | 165 | 166 | 166 |
|-----------------|-----|-----|-----|-----|-----|
| Group B heights | 161 | 162 | 164 | 165 | 175 |

(3) The dance team needs to select five students to participate in a competition. Three students have already been selected with heights of 168, 168, and 172. The variance of their heights is 32/9. When selecting the other two students, it is first required that the variance of the heights of the five students (including the three selected) is less than 32/9. Secondly, it is required that the average height of the five students is maximized. The heights of the other two selected students are ______ and ______.

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