
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
Four cubes with edge lengths $2$, $3$, $4$, and $5$ are stacked vertically. Each cube's bottom face is on the $xy$-plane, and one vertex of each cube is at the origin $(0,0,0)$. Point $X$ is at the origin $(0,0,0)$, and point $Y$ at $(5,5,14)$. What is the length of the portion of $\overline{XY}$ contained in the cube with edge length $4$?
- **A)** $4$
- **B)** $6\sqrt{2}$
- **C)** $4\sqrt{3}$
- **D)** $5\sqrt{2}$
- **E)** $7$

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