
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 positive integers \(a, b, c\) that satisfy the equation
\[ 
10a^2 - 3ab + 7c^2 = 0,
\]
find the minimum value of \((a, b)(b, c)(c, a)\).

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