
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
There are four propositions as follows:  
① Group A and Group B have the following data: A: $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$; B: $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$. The medians of Group A and Group B are $5$ and $5.5$ respectively.  
② The correlation coefficient is $r=-0.88$, indicating a weak correlation between the two variables.  
③ If the observed value of $k^{2}$ calculated from the data in a $2\times 2$ contingency table is approximately $4.567$, it is considered that the two variables are related, with a probability of making this inference incorrectly not exceeding $0.05$.  
Attachment:  

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

④ After obtaining the regression line equation $\hat{y}=\hat{b}x+\hat{a}$ for a set of data $(x_{i}$, $y_{i})\left(i=1,2,\cdots ,n\right)$ using the least squares method, residual analysis should be performed. The residual of the corresponding data $(x_{i}$, $y_{i})\left(i=1,2,\cdots ,n\right)$ in residual analysis is defined as $\hat{{e}}_{i}={y}_{i}-(\hat{b}{x}_{i}+\hat{a})$.  
The incorrect propositions are ____.

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