
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
Lucas collects minerals for his geological study. He arranges the same number of minerals on each shelf, and then places these shelves into three different cabinets. The first cabinet contains a total of 924 minerals, the second contains 1386 minerals, and the third contains 462 minerals. What is the largest number of minerals that Lucas could be placing on each shelf?

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