
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
Which of the following statements is incorrect for the correlation coefficient $r$?  
① When $r=0$, the linear relationship between paired sample data is weak;  
② When $r \gt 0$, it indicates that the paired sample data is positively correlated;  
③ If the regression coefficient $\hat{b}＜0$ in the linear regression equation, then the correlation coefficient $r \gt 0$;  
④ The closer $|r|$ is to $1$, the stronger the linear correlation, and the closer $|r|$ is to $0$, the weaker the linear correlation.

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