
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
Right-angled triangular pyramids, referred to as "right-angle pyramids," are characterized by their lateral edges being perpendicular to each other. The lateral faces and the base face of such a pyramid are termed "right-angle faces" and "slant faces," respectively. Any cross-section of a slant face that passes through the pyramid's apex and the midpoints of any two edges of the slant face is coined the "midsection" of the slant face.

1. A right-angled triangle has the property: "The sum of the squares of the lengths of the two right-angle sides equals the square of the length of the hypotenuse."
    By analogy, state the property that a right-angle pyramid possesses: __________.

2. A right-angled triangle has the property: "The length of the median to the hypotenuse is equal to half the length of the hypotenuse."
    By analogy, state the property that a right-angle pyramid possesses: __________.

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