
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 physical education class, a group of male students from a certain class took a $100m$ running test, with the passing time being $15s$. The table below reflects the performance of $10$ male students in the group (unit: $s$), with scores higher and lower than $15s$ recorded as positive and negative, respectively.

| Number | 1 | 2 | 3 | 2 | 2 |
|--------|---|---|---|---|---|
| Difference ($/s$) |  | $+1$ | $-1.2$ | $0$ | $-0.4$ |

$(1)$ If one male student's score was tampered with, but it is known that his test score is $15.8s$, then the value in the table where tampering occurred is ______.

$(2)$ What is the average score in seconds for this group of male students?

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