
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: $\sqrt {1\cdot 2} < \frac {3}{2}$, $\sqrt {1\cdot 2}+ \sqrt {2\cdot 3} < 4$, $\sqrt {1\cdot 2}+ \sqrt {2\cdot 3}+ \sqrt {3\cdot 4} < \frac {15}{2}$, $\sqrt {1\cdot 2}+ \sqrt {2\cdot 3}+ \sqrt {3\cdot 4}+ \sqrt {4\cdot 5} < 12$, ...
Following this pattern, the $n$th inequality is \_\_\_\_\_\_.

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