
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 triangular pyramid with mutually perpendicular lateral edges is called a "right-angle triangular pyramid." The sides and base of the triangular pyramid are referred to as its "right-angle sides and slant sides," respectively. A cross-section passing through the vertex of the triangular pyramid and the midpoints of any two sides on a slant side is called the "midsection" of that slant side. By analogy with the following properties of a right-angle triangle:  
(1) The length of the midline to the hypotenuse is equal to half of the hypotenuse length;  
(2) The sum of the squares of the lengths of the two legs is equal to the square of the hypotenuse length;  
(3) The sum of the squares of the cosines of the angles between the hypotenuse and the two legs is equal to 1.  
Write out the corresponding properties (at least one) for a right-angle triangular pyramid: ________.

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