
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 space, points \( A, B, C, \) and \( D \) are given such that \( |AB| = |BC| = |CD| \) and \( \angle ABC = \angle BCD = \angle CDA = \alpha \). Find the angle between the lines \( AC \) and \( BD \).

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