
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
Given the center of the base of a regular triangular pyramid as point $O$ and the points of intersection of a moving plane $QRS$ with the three lateral edges or their extensions as $Q$, $R$, $S$, calculate the sum $\frac{1}{PQ}+\frac{1}{PR}+\frac{1}{PS}$.

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