
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
According to the notice from the Ministry of Industry and Information Technology on the comprehensive promotion of China's characteristic enterprise new apprenticeship system and the strengthening of skills training, our region clearly promotes the new apprenticeship system training for all types of enterprises, deepens the integration of production and education, school-enterprise cooperation, and the apprenticeship training goal is to cultivate intermediate and senior technical workers that meet the needs of business positions. In the year 2020, a certain enterprise needs to train 200 apprentices. After the training, an assessment is conducted, and the statistics of obtaining corresponding job certificates are as follows:

| Job Certificate | Junior Worker | Intermediate Worker | Senior Worker | Technician | Senior Technician |
|-----------------|---------------|---------------------|--------------|-----------|------------------|
| Number of People | 20 | 60 | 60 | 40 | 20 |

$(1)$ Now, using stratified sampling, 10 people are selected from these 200 people to form a group for exchanging skills and experiences. Find the number of people in the exchange group who have obtained job certificates in the technician category (including technicians and senior technicians).

$(2)$ From the 10 people selected in (1) for the exchange group, 3 people are randomly chosen as representatives to speak. Let the number of technicians among these 3 people be $X$. Find the probability distribution and the mathematical expectation of the random variable $X$.

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