
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
In the tetrahedron \( A B C D \), \( \triangle A D B \) is an isosceles right triangle with \( A D = 1 \), \( \angle A D B = 90^{\circ} \). Additionally, \( \angle B D C = \angle A D C = 60^{\circ} \). Find the distance between the skew lines \( A B \) and \( C D \).

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