
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:
$$\begin{matrix}1+ \frac {1}{2^{2}} < \frac {3}{2}, \\ 1+ \frac {1}{2^{2}}+ \frac {1}{3^{2}} < \frac {5}{3}, \\ 1+ \frac {1}{2^{2}}+ \frac {1}{3^{2}}+ \frac {1}{4^{2}} < \frac {7}{4} \\ \vdots \end{matrix}$$
We can induce an inequality that holds for all positive integers $n > 1$: $1+ \frac {1}{2^{2}}+ \frac {1}{3^{2}}+ \dots +\frac {1}{n^{2}} < f(n)$. Determine the expression for the right-hand side of the inequality, $f(n)$.

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