
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
Three young "highway robbers," on their way back from the movies, encountered a woman selling apples. Tom grabbed half of all the apples but threw 10 back into the basket. Ben took a third of the remaining apples but returned 2 apples he didn't like. Jim took half of the remaining apples but threw back a wormy one. The woman ended up with only 12 apples in her basket.

How many apples did the woman have before the encounter?

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