
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
Given a parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$. Point $X$ is chosen on edge $A_{1} D_{1}$, and point $Y$ is chosen on edge $B C$. It is known that $A_{1} X=5$, $B Y=3$, and $B_{1} C_{1}=14$. The plane $C_{1} X Y$ intersects ray $D A$ at point $Z$. Find $D Z$.

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