
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
Credit refers to a kind of production relationship and social relationship of mutual trust formed between people, units, and commodity transactions. Good credit plays an important role in the development of individuals and society. A certain place implements a credit scoring system, dividing credit scores into five levels from high to low. Credit scores exceeding 150 points are considered excellent credit; credit scores within the range of (120, 150] are considered good credit; credit scores within the range of (100, 120] are considered fair credit; credit scores within the range of (80, 100] are considered slight default; and credit scores not exceeding 80 points are considered poor credit. After implementing the credit scoring system for a period of time, in order to understand the effectiveness of the system, the local government randomly selected 200 residents and obtained their credit score data as shown in the table below.

| Credit Level | Excellent | Good | Fair | Slight Default | Poor |
|--------------|-----------|------|------|----------------|------|
| Number       | 25        | 60   | 65   | 35             | 15   |

$(1)$ From these 200 residents, 2 people are randomly selected. Find the probability that both of these 2 people have excellent credit.  
$(2)$ To strengthen the credit scoring system, the local government provides $100 electronic consumption vouchers to residents with excellent credit and $50 vouchers to residents with good or fair credit, while residents with slight default or poor credit do not receive any vouchers. If the frequencies of each credit level in the table are considered as the corresponding probabilities, and 2 people are randomly selected from the residents, let X be the total amount of vouchers received by these 2 people. Find the distribution table and expectation of X.

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