
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 inequality series $1+ \frac {1}{4} < \frac {3}{2},1+ \frac {1}{4}+ \frac {1}{9} < \frac {5}{3},1+ \frac {1}{4}+ \frac {1}{9}+ \frac {1}{16} < \frac {7}{4},…$, summarize the $n(n∈N^{*})$th inequality.

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