
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
A school is numbering lockers for students from 300 to 350 and plans to label additional lockers for sports equipment from 400 to 450. Each locker number requires separate digits, and digits are sold in packages containing one of each digit from 0 through 9. How many packages does the school need to purchase?

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