
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

Suppose that

$$
\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right) \cdots\left(1+\frac{1}{k}\right)\left(1+\frac{1}{k+1}\right)=2014
$$

for some positive integer \( k \). (There are \( k \) factors in the product.) What is the value of \( k \)?

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