
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
To support the Hope Project in impoverished mountainous areas, a school organized students to prepare 1710 notebooks, 664 pens, and several sets of protractors. The students divided these learning supplies into three types of packages, labeled as A, B, and C, for mailing. Each A-type package contains 10 notebooks, 8 pens, and 6 protractors; each B-type package contains 15 notebooks, 2 pens, and 7 protractors; and each C-type package contains 20 notebooks, 8 pens, and 10 protractors. It is known that the quantities of A, B, and C packages are all positive integers, and the number of A-type packages is greater than 31, and the number of C-type packages is greater than 33. Then, the total number of protractors in all packages is ____.

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