
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
Consider a $5 \times 6 \times 4$ rectangular parallelepiped with vertex $H$ positioned at $(0,0,0)$, and vertices $E$, $F$, and $G$ at $(5,0,0)$, $(0,6,0)$, and $(0,0,4)$ respectively. Find the perpendicular distance from $H$ to the plane containing vertices $E$, $F$, and $G$.

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