
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 right triangle $ABC$, the two legs are $a$ and $b$, respectively. Let $h$ be the height to the hypotenuse, then $\dfrac {1}{h^{2}}= \dfrac {1}{a^{2}}+ \dfrac {1}{b^{2}}$. By analogy, in a triangular pyramid $S-ABC$ with three lateral edges $SA$, $SB$, and $SC$ being mutually perpendicular and their lengths being $a$, $b$, and $c$, respectively, let $h$ be the height from the apex to the base $ABC$, then ______.

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