
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:
$$\sqrt{1\times 2} < 2,\;\sqrt{1\times 2}+\sqrt{2\times 3} < \frac{9}{2},\;\sqrt{1\times 2}+\sqrt{2\times 3}+\sqrt{3\times 4} < 8,\;\sqrt{1×2}+ \sqrt{2×3}+ \sqrt{3×4}+ \sqrt{4×5} < \frac{25}{2},\;\ldots$$
Based on the pattern, determine the $n$-th inequality.

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