
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
For a tetrahedron with a volume of $V$, the area of the $i$-th face is denoted as $S_i$ ($i=1, 2, 3, 4$), and the distance from any point $Q$ inside the tetrahedron to the $i$-th face is denoted as $H_i$ ($i=1, 2, 3, 4$). If $\frac{S_1}{1} = \frac{S_2}{2} = \frac{S_3}{3} = \frac{S_4}{4} = K$, then $H_{1}+2H_{2}+3H_{3}+4H_{4}$ equals

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