
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
Jessica and Tina are both avid book collectors. Their respective collections share twelve of the same books. Jessica has twenty-two books in her collection. Ten books are in Tina's collection but not Jessica's. How many books are in either Jessica's or Tina's collection, but not both?

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