
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 triangle \(ABC\), the ratio \(|BC| : |AC| = 3\) and \(\angle ACB = \alpha\). Points \(D\) and \(K\) are taken on side \(AB\) such that \(\angle ACD = \angle DCK = \angle KCB\). Find \(|CD| : |CK|\).

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