
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
Ming, Catherine, and Luke went shopping for pencils. Ming bought 30 pencils, Catherine bought 45 pencils, and Luke bought 75 pencils. If each package of pencils sold at the store contains the same number of pencils and each can only buy complete packages, find the largest possible number of pencils in a package.

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