
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 \(n\)th term in a certain sequence is calculated by multiplying together all the numbers \(\sqrt{1+\frac{1}{k}}\), where \(k\) takes all the integer values from 2 to \(n+1\) inclusive. For example, the third term in the sequence is \(\sqrt{1+\frac{1}{2}} \times \sqrt{1+\frac{1}{3}} \times \sqrt{1+\frac{1}{4}}\). Which is the smallest value of \(n\) for which the \(n\)th term of the sequence is an integer?
A 3
B 5
C 6
D 7
E more than 7

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