
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:

$(1)$ $+ \dfrac{1}{{2}^{2}} < \dfrac{3}{2}$

$(1)$ $+ \dfrac{1}{{2}^{2}} + \dfrac{1}{{3}^{2}} < \dfrac{5}{3}$

$(1)$ $+ \dfrac{1}{{2}^{2}} + \dfrac{1}{{3}^{2}} + \dfrac{1}{{4}^{2}} < \dfrac{7}{4}$

$(\ldots)$

Following this pattern, when $n \in \mathbb{N}^{*}$, $1 + \dfrac{1}{{2}^{2}} + \dfrac{1}{{3}^{2}} + \ldots + \dfrac{1}{{(n+1)}^{2}} < \_$.

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