
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
On Lucy's $10^{\text{th}}$ birthday in 2012, her mother told her, "I am now five times as old as you are." In what year will Lucy's mother be able to say, "My age is now twice your age," on Lucy's birthday?

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