
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
甲、乙两校分别有$120$名、$100$名学生参加了某培训机构组织的自主招生培训,考试结果出来以后,培训机构为了进一步了解各校所培训学生通过自主招生的情况,从甲校随机抽取$60$人,从乙校随机抽取$50$人进行分析,相关数据如表.

|          | 通过人数 | 未通过人数 | 总计 |
|----------|---------|---------|------|
| 甲校     |         |         |      |
| 乙校     | $30$    |         |      |
| 总计     |         | $60$    |      |

$\left(1\right)$完成上面$2\times 2$列联表,并据此判断是否有$99\%$的把握认为自主招生通过情况与学生所在学校有关；

（2）现从甲、乙两校通过的学生中采取分层抽样的方法抽取$5$人,再从所抽取的$5$人种随机抽取$2$人,求$2$人全部来自于乙校的概率.

参考公式:$K^{2}=\dfrac{n\left(ad-bc\right)^{2}}{\left(a+b\right)\left(c+d\right)\left(a+c\right)\left(b+d\right)}$,$n=a+b+c+d$.

参考数据:

| $P\left(K^{2}\geqslant k_{0}\right)$ | $0.15$ | $0.10$ | $0.05$ | $0.025$ | $0.010$ | $0.005$ | $0.001$ |
|--------------------------------------|-------|-------|-------|--------|--------|--------|--------|
| $k_{0}$                              | $2.072$ | $2.706$ | $3.841$ | $5.024$ | $6.635$ | $7.879$ | $10.828$ |

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