
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
Let a quadrilateral with area $S$ have its $i$-th side length denoted as $a_i (i=1,2,3,4)$, and let $P$ be any point within the quadrilateral. The distance from point $P$ to the $i$-th side is denoted as $h_i$. If $\dfrac{a_1}{1}= \dfrac{a_2}{2}= \dfrac{a_3}{3}= \dfrac{a_4}{4}=k$, then $\sum\limits_{i=1}^{4}\left(ih_1\right)= \dfrac{2S}{k}$. By analogy, for a tetrahedron with volume $V$ and its $i$-th face area denoted as $S_i (i=1,2,3,4)$, and $Q$ being any point within the tetrahedron, the distance from point $Q$ to the $i$-th face is denoted as $H_i$, the corresponding correct proposition is: If $\dfrac{S_1}{1}= \dfrac{S_2}{2}= \dfrac{S_3}{3}= \dfrac{S_4}{4}=k$, then ______________.

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