
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 side \( AC = 5 \) cm, \( BC - AB = 2 \) cm, and \( \angle A : \angle C = 2 \). Find the lengths of sides \( AB \) and \( BC \).

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