
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
On April 7, 2021, the "Study Strong Country" launched the "Strong Country Doctor" function, providing various medical and health services such as intelligent guidance, self-examination of diseases, disease encyclopedia, and health promotion.

1. In order to understand the relationship between the number of times "Strong Country Doctor" is used and gender, a certain survey agency surveyed 200 users of "Strong Country Doctor" and obtained the data in the table below. Complete the table based on the given data and determine whether there is a 99.9% certainty that the number of times "Strong Country Doctor" is used is related to gender.

   |            | Male | Female | Total |
   |------------|------|--------|-------|
   | High Usage | 40   |        |       |
   | Low Usage  |      | 30     |       |
   | Total      | 90   |        | 200   |

2. The agency collected data on the number of female users who used the service each day within 7 days of the launch of "Strong Country Doctor." On the x-th day after the launch, the number of female users using "Strong Country Doctor" was y, and the data is as follows:

   | x   | 1   | 2   | 3   | 4   | 5   | 6    | 7    |
   |-----|-----|-----|-----|-----|-----|------|------|
   | y   | 6   | 11  | 21  | 34  | 66  | 100  | 195  |

   By observing the scatter plot, it was found that the sample points are concentrated around a curve of the form y = a * b^x. Find the regression equation of y with respect to x and predict the number of female users who will use the service on the 12th day after the launch of "Strong Country Doctor."

   Given: Random variable ${x^2}=\frac{{n{{({ad-bc})}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$, where $n=a+b+c+d$.

   | $P(x^{2}\geqslant k_{0})$ | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
   |---------------------------|------|-------|------|-------|-------|
   | $k_{0}$                   | 3.841| 5.024 | 6.635| 7.879 | 10.828|
   |                           |      |       |      |       |       |
   | $\overline{y}$            | $\overline{z}$ | $\sum_{i=1}^7{{x_i}{z_i}}$ | $\sum_{i=1}^7{{x_i}{y_i}}$ | $10^{0.6}$ |
   | 61.9                      | 1.6  | 51.8 | 2522 | 3.98  |

   where $z_{i}=\lg y_{i}$.

   Reference formula: For a set of data $(x_{1}$,$y_{1})$,$(x_{2}$,$y_{2})$,$\ldots $,$(x_{n}$,$y_{n})$, the least squares estimates of the slope and intercept of the regression line $\hat{y}=\hat{c}+\hat{d}x$ are $\hat{d}=\frac{{\sum_{i=1}^n{({{x_i}-\overline{x}})({{y_i}-\overline{y}})}}}{{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}}}}$ and $\hat{c}=\overline{y}-\hat{d}\overline{x}$.

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