
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
A right-angled triangular pyramid, also known as a "right triangular pyramid," is one in which the lateral edges are perpendicular to each other, and the side faces and the base face are called the "right-angle faces and oblique face" of the right triangular pyramid, respectively. In a right-angled triangle, the lengths of the sides forming the right angle are $a$ and $b$, and the length of the hypotenuse is $c$. The triangle has the property: $c^2 = a^2 + b^2$. By analogy, write down the property that a right triangular pyramid should have, with the areas of the right-angle faces being $S_1$, $S_2$, $S_3$, and the area of the oblique face being $S$:

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