
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
In an arithmetic sequence of positive integers \(a_{1}, a_{2}, \cdots\), for each \(n\), the product \(a_{n} a_{n+31}\) is divisible by 2005. Can it be asserted that "every term in the sequence is divisible by 2005"?

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