
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 schooner travels from $A$ to $B$ across a lake, and then from $B$ to $C$ upstream along a river before returning. The schooner's speed relative to still water is always maintained at $c$ km/h. The journey from $A$ to $C$ takes $\alpha$ hours, and the return journey takes $\beta$ hours. Additionally, the time taken for the schooner to travel from $C$ to $B$ is three times less than the time taken to travel from $B$ to $A$. Find the distances $AB$ and $BC$.

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