
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 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 solid geometry: In the tetrahedron $O-ABC$, where $\angle AOB=\angle BOC=\angle COA=90^{\circ}$, $S$ is the area of the face opposite to vertex $O$, and $S_{1}$, $S_{2}$, $S_{3}$ are the areas of the side faces $\triangle OAB$, $\triangle OAC$, and $\triangle OBC$ respectively. The relationship that $S$, $S_{1}$, $S_{2}$, and $S_{3}$ satisfy is ______.

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