
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 parallelepiped \( ABCD A_{1} B_{1} C_{1} D_{1} \) is given. A point \( X \) is chosen on edge \( A_{1} D_{1} \) and a point \( Y \) is chosen on edge \( BC \). It is known that \( A_{1}X = 5 \), \( BY = 3 \), and \( B_{1} C_{1} = 14 \). The plane \( C_{1}XY \) intersects the ray \( DA \) at point \( Z \). Find \( DZ \).

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