
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
The sum of three numbers $a$, $b$, and $c$ is 240. When the smallest number $a$ is multiplied by 6, the result is $m$. The value $m$ equals the largest number $b$ when subtracted by 12, and equals the second largest number $c$ when added by 12. What is the product of the three numbers?

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