
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 the following inequalities:

\\(1+ \\dfrac{1}{2}+ \\dfrac{1}{3} < 2 \\)

\\(1+ \\dfrac{1}{2}+ \\dfrac{1}{3}+...+ \\dfrac{1}{7} < 3 \\)

\\(1+ \\dfrac{1}{2}+ \\dfrac{1}{3}+...+ \\dfrac{1}{15} < 4 \\)

\\(........\\)

Find the value of \\(n\\) such that \\(1+\\dfrac{1}{2}+\\dfrac{1}{3}+\\ldots +\\dfrac{1}{{{2}^{n+1}}-1} < \\)\_\_\_\_\_\_\_\_\\(.(n∈N\*)\\)

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