
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
Four years ago, Aaron was twice as old as his sister Beth, and six years ago, Aaron was three times as old as Beth. Determine the number of years after which the ratio of their ages will be $3 : 2$.

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