
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
Given that a piece of purple candy costs $30$ cents, and Casper has enough money to buy $16$ pieces of red candy, $18$ pieces of yellow candy, or $20$ pieces of black candy, determine the smallest possible value of $m$ if he can also buy $m$ pieces of purple candy.

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