
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+\\dfrac{1}{{{2}^{2}}} < \\dfrac{3}{2}, \\\\ & 1+\\dfrac{1}{{{2}^{2}}}+\\dfrac{1}{{{3}^{2}}} < \\dfrac{5}{3}, \\\\ & 1+\\dfrac{1}{{{2}^{2}}}+\\dfrac{1}{{{3}^{2}}}+\\dfrac{1}{{{4}^{2}}} < \\dfrac{7}{4}, \\\\ \\end{matrix}\\)

...

A general inequality can be inferred for positive integers $n > 1$: $1+\dfrac{1}{{{2}^{2}}}+\dfrac{1}{{{3}^{2}}}+…+\dfrac{1}{{{n}^{2}}} < f(n)$. Determine the expression for the right side of the inequality, $f(n)$.

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