
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
Observe the following inequalities:

  \\(① \dfrac{1}{\sqrt{2}} < 1\\); \\(② \dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{6}} < \sqrt{2}\\); \\(③ \dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{6}}+\dfrac{1}{\sqrt{12}} < \sqrt{3}…\\), then the fifth inequality is \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

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