
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 statements, the correct one is \_\_\_\_\_\_\_\_\_\_\_\_

(1) In regression analysis models, the larger the residual sum of squares, the better the model fit.
(2) The larger the absolute value of the linear correlation coefficient $|r|$, the stronger the linear correlation between the two variables; conversely, the weaker the linear correlation.
(3) The variance remains unchanged when a constant is added to or subtracted from each data point in a dataset.
(4) Given that $S_k = \frac{1}{k+1} + \frac{1}{k+2} + \frac{1}{k+3} + \dots + \frac{1}{2k}$, then $S_{k+1} = S_k + \frac{1}{2(k+1)}$.
(5) In calculating the relationship between smoking and lung disease, these two categorical variables, if we know from the independence test that there is a $99\%$ chance that smoking is related to lung disease, then we can say that someone who smokes has a $99\%$ chance of having lung disease.
(6) The area of a triangle is given by $S = \frac{1}{2}(a + b + c) \cdot r$ ($a$, $b$, $c$ are the lengths of the triangle, and $r$ is the radius of the incircle). By analogy, we can derive that the volume of a tetrahedron is $V = \frac{1}{3}(S_1 + S_2 + S_3 + S_4) \cdot r$ ($S_1, S_2, S_3, S_4$ are the areas of the four faces of the tetrahedron, and $r$ is the radius of the insphere).

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