
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 structure consists of four cubes with edge lengths $2$, $3$, $4$, and $5$, stacked vertically in decreasing size from bottom to top, with each upper cube centered on the one below it. If a line segment $\overline{XY}$ starts from the bottom left corner of the largest cube (bottom-most) at $(0,0,0)$ and ends at the top right corner of the smallest cube (top-most) at $(5,5,14)$, what is the length of the portion of $\overline{XY}$ contained within the cube with edge length $4$?
A) $\sqrt{18}$
B) $\sqrt{20.5}$
C) $\sqrt{22.5}$
D) $\sqrt{24.5}$

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