
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]

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# Your action step 2

# Your action step 3

...

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The 19th Asian Games Organizing Committee announced that the Asian Games will be held in Hangzhou from September 23 to October 8, 2023. For this event, a school organized basketball and volleyball competitions with the theme "Welcoming the Asian Games." Each student could only sign up for one event. A research group randomly selected 100 male students and 100 female students from those who signed up for the competitions for interviews. Those who participated in the volleyball competition were classified as Group A, and those who participated in the basketball competition were classified as Group B. The investigation found that there were 96 members in Group A, including 36 males.

1. Based on the above data, complete the 2x2 contingency table and analyze whether students' preference for volleyball or basketball is related to their "gender" based on the independence test with a small probability value of $\alpha = 0.001$.
2. Now, from the surveyed male students, 25 people were selected using stratified sampling. From these 25 people, 3 people were randomly selected to receive gifts. The number of people in Group A among the 3 recipients is denoted as X. Find the distribution table and mathematical expectation of X.

Reference formula: ${\chi^2}=\frac{{n{{(ad-bc)}^2}}}{{({a+b})({c+d})({a+c})({b+d})}},n=a+b+c+d$.
Reference data:
| $\alpha $ | $0.1$ | $0.05$ | $0.01$ | $0.005$ | $0.001$ |
|-----------|-------|--------|--------|---------|---------|
| $x_{\alpha }$ | $2.706$ | $3.841$ | $6.635$ | $7.841$ | $10.828$ |

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