
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
In a class of 16 male students in the first year of junior high school, their heights were measured during a physical examination. Using $160cm$ as the reference point, the heights of the male students were recorded. Heights above $160cm$ were recorded as positive, and heights below $160cm$ were recorded as negative. The relative heights (in cm) of the first 15 male students are recorded in the table below. The height of the 16th male student is $171cm$.

| Serial Number | 1   | 2   | 3   | 4    | 5   | 6   | 7   | 8   |
|---------------|-----|-----|-----|------|-----|-----|-----|-----|
| Relative Height| -7 | +4 | 0   | +16  | +2  | -3  | +1  | -5  |
| Serial Number | 9   | 10  | 11  | 12   | 13  | 14  | 15  | 16  |
| Relative Height| -9 | +3 | -4  | +7   | +1  | -2  | +1  | $m$ |

$(1)$ In the table, $m=$______;<br/>
$(2)$ The height difference between the tallest and shortest male students in the class is ______$cm$;<br/>
$(3)$ Calculate the average height of the male students in the class.

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