
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 certain mechanism consists of 30 parts, some of which are large and some of which are small. It is known that among any 12 parts taken, there will always be at least one small part, and among any 20 parts, there will always be at least one large part. How many large and small parts does the mechanism contain?

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