
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
Let \( a, b, c \) be natural numbers such that the product \( ab \) is divisible by \( 5c \), the product \( c \) is divisible by \( 13a \), and the product \( ca \) is divisible by \( 31b \). Find the smallest possible value of the product \( abc \). Justify your answer.

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