
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 the ray \(D A\) at point \(Z\). Find \(D Z\).

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