
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
What is the minimum value of the product
\[ \prod_{i=1}^{6} \frac{a_{i} - a_{i+1}}{a_{i+2} - a_{i+3}} \]
given that \((a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6})\) is a permutation of \((1, 2, 3, 4, 5, 6)\)? (Note: \(a_{7} = a_{1}, a_{8} = a_{2}, \ldots\))

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