
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 $5 \times 3 \times 2$ rectangular parallelepiped with vertices $D$, $A$, $B$, and $C$ such that $D$ is at $(0,0,0)$, $A$ at $(5,0,0)$, $B$ at $(0,3,0)$, and $C$ at $(0,0,2)$. Calculate the perpendicular distance from vertex $D$ to the plane containing vertices $A$, $B$, and $C$.

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