
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
In planar geometry, it is stated that for a right-angled triangle $ABC$ with two sides of length $a$ and $b$, and an altitude $h$ on the hypotenuse, the following relationship holds: $\frac{1}{a^{2}}+ \frac{1}{b^{2}}= \frac{1}{h^{2}}$. Extend this to three-dimensional space: given a right triangular pyramid $A-BCD$ with pairwise perpendicular side edges of lengths $a$, $b$, and $c$, and an altitude $h$ on the face $BCD$, we have ____.

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