
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
Since the outbreak of the epidemic, mobile payment, as a more convenient, fast, and contactless payment method compared to cash payment, has been favored by more and more consumers and merchants. A financial institution randomly selected 100 residents from a certain city to investigate whether "the choice of payment method is related to age." Some of the statistical data obtained from the survey are shown in the table below:

|           | Mobile Payment | Cash Payment | Total |
|-----------|----------------|--------------|-------|
| Under 60  | 40             | 10           | 50    |
| 60 and over | 30           | 20           | 50    |
| Total     | 70             | 30           | 100   |

$(1)$ Based on the data above, determine whether there is a 99% confidence that the choice of payment method is related to age;  
$(2)$ Considering frequency as probability, now randomly select 1 person from residents aged 60 and over in the city for 3 times. Let $X$ be the number of people who choose "Cash Payment" out of the 3 selected individuals. If the results of each selection are independent, find the distribution table of $X$, the mathematical expectation $E(X)$, and the variance $D(X)$.  
Reference formula: ${K^2}=\frac{{n{{({ad-bc})}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$, where $n=a+b+c+d$.

| $P(K^{2}\geqslant k_{0})$ | 0.10 | 0.050 | 0.010 | 0.001 |
|---------------------------|------|-------|-------|-------|
| $k_{0}$                   | 2.706| 3.841 | 6.635 | 10.828|

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