
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
Confucius said: "By three methods we may learn wisdom: First, by reflection, which is noblest; Second, by imitation, which is easiest; and third by experience, which is the bitterest." The study of mathematics is also like this. In order to investigate the relationship between "excellent math performance" and "timely review," a volunteer from a certain school randomly selected 60 students from the second year of high school for a questionnaire survey, and obtained the following sample data:

|                    | Excellent Math Performance (Number of Students) | Not Excellent Math Performance (Number of Students) |
|--------------------|-------------------------------------------------|----------------------------------------------------|
| Timely Review      | 24                                              | 6                                                  |
| Not Timely Review  | 8                                               | 22                                                 |

$(Ⅰ)$ Based on the small probability value $\alpha = 0.001$ of the independence test, can it be concluded that there is a relationship between "excellent math performance" and "timely review"?

$(Ⅱ)$ In this sample, using stratified sampling method, 8 students are selected from those with excellent math performance, and then 3 students are randomly selected from these 8 students. Let the number of students who review timely among the 3 selected be $X$. Find the distribution table and mathematical expectation of $X$.

Critical value reference table:

| $\alpha$ | $0.10$ | $0.05$ | $0.025$ | $0.010$ | $0.005$ | $0.001$ |
|----------|--------|--------|---------|---------|---------|---------|
| $x_{\alpha}$ | $2.706$ | $3.841$ | $5.024$ | $6.635$ | $7.879$ | $10.828$ |

(Reference formula: $\chi ^{2}=\frac{n(ad-bc)^2}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$)

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