
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
The school lent 105 books to the sixth-grade students, one book per student. If the books are lent to the boys first and the remaining to the girls, only $$\frac {1}{3}$$ of the girls can borrow a book. If the books are lent to the girls first and the remaining to the boys, then half of the boys cannot borrow a book. How many students are there in the sixth grade in total?

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