
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
Lucy and her five friends are ages $4$, $6$, $8$, $10$, $12$, and $14$. Given that two of her friends whose ages sum to $18$ went to the skatepark, two friends less than $12$ went to the swimming pool, and Lucy and the $6$-year-old went to the library, determine Lucy's age.

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