
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 expressions: $\sqrt{1 \times 2} < 2$, $\sqrt{1 \times 2} + \sqrt{2 \times 3} < \frac{9}{2}$, $\sqrt{1 \times 2} + \sqrt{2 \times 3} + \sqrt{3 \times 4} < 8$, $\sqrt{1 \times 2} + \sqrt{2 \times 3} + \sqrt{3 \times 4} + \sqrt{4 \times 5} < \frac{25}{2}$,  
..., according to the above pattern, the $n$th inequality is __________.

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