
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 $1$, $3$, $5$, and $7$ are stacked upon one another. The bottom face of each cube lies on the $xy$-plane, and one vertex of each cube is at the origin $(0,0,0)$. If a line segment $\overline{XY}$ runs from point $X$ at $(0,0,0)$ to point $Y$ at $(7,7,16)$, find the length of $\overline{XY}$ that is contained within the cube that has edge length $5$.
A) $6\sqrt{3}$
B) $2\sqrt{3}$
C) $5\sqrt{3}$
D) $3\sqrt{3}$
E) $4\sqrt{3}$

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