
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
If \(a\), \(b\), and \(c\) are the three sides of a right triangle with \(c\) being the hypotenuse, then \(a^2 + b^2 = c^2\), which is known as the Pythagorean theorem. Now, let's extend this theorem to three-dimensional geometry: In the tetrahedron \(O\)-\(ABC\), where \(\angle AOB = \angle BOC = \angle COA = 90°\), \(S\) is the area of the face opposite to vertex \(O\), \(S_1\), \(S_2\), and \(S_3\) are the areas of the side faces \(\triangle OAB\), \(\triangle OAC\), and \(\triangle OBC\) respectively, then the relationship between \(S\), \(S_1\), \(S_2\), and \(S_3\) is \_\_\_\_\_\_.

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