
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
A cube with side length 15 is suspended above a plane. The vertex closest to the plane is labeled $A$. The three vertices adjacent to vertex $A$ are at heights 18, 20, and 22 above the plane. Find the expression for the distance from vertex $A$ to the plane in the form $\frac{r-\sqrt{s}}{t}$, where $r$, $s$, and $t$ are positive integers, and compute $r+s+t$.

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