
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
Let $\triangle ABC$ have internal angles $A$, $B$, and $C$, with the sides opposite these angles being $a$, $b$, and $c$, respectively. If the lengths of the sides are three consecutive positive integers, and $A > B > C$, with $3b = 20a\cos A$, then the ratio $\sin A : \sin B : \sin C$ is \_\_\_\_\_\_\_\_.

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