
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
The ages of grooms and brides applying for marriage certificates in a certain area within a week are recorded as (groom's age $y$, bride's age $x$):  
(37, 30), (30, 27), (65, 56), (45, 40), (32, 30), (28, 26), (45, 31), (29, 24), (26, 23), (28, 25), (42, 29), (36, 33), (32, 29), (24, 22), (32, 33), (ZI, 29), (37, 46), (28, 25), (33, 34), (21, 23), (24, 23), (49, 44), (28, 29), (30, 30), (24, 25), (22, 23), (68, 60), (25, 25), (32, 27), (42, 37), (24, 24), (24, 22), (28, 27), (36, 31), (23, 24), (30, 26)  
Consider the regression problem of $y$ with respect to $x$:  
(1) If every groom and bride were of the same age, what would be the slope and intercept of the regression line through these points?  
(2) If every groom was 5 years older than his bride, what would be the slope and intercept of the regression line through these points?  
(3) If every groom was 10% older than his bride, what would be the slope and intercept of the regression line through these points?  
(4) Draw the regression line for the actual ages above;  
(5) What conclusion can you draw about the age model of brides and grooms from this regression line?

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