
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
Among the following propositions, the correct one(s) is(are) _________________

(1) The hypothesis of the chi-square independence test is that two events are independent,

(2) When studying the relationship between smoking and chronic bronchitis in people over 50 years old, the chi-square statistic calculated from a $2 \times 2$ contingency table is $7.469 > 6.635$, so there is a 99% confidence that chronic bronchitis is related to smoking habits. This means that out of 100 people over 50 years old, 99 have chronic bronchitis;

(3) The higher the correlation coefficient $R^{2}$ used to describe the effect of regression, the better. The larger the value of $R^{2}$, the smaller the residual sum of squares, and the better the model fit.

(4) Given a random variable $X \sim N(\mu,\rho^{2})$, the smaller $\rho$ is, the higher the probability that $X$ is concentrated around $\mu$;

(5) There exists $x_{0} \in \mathbb{R}$, such that $\sin x_{0} + \cos x_{0} > \sqrt{2}$;

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