
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 $S_{1}=1+\frac{1}{{1}^{2}}+\frac{1}{{2}^{2}}$, $S_{2}=1+\frac{1}{{2}^{2}}+\frac{1}{{3}^{2}}$, $\ldots$, $S_{n}=1+\frac{1}{{n}^{2}}+\frac{1}{{(n+1)}^{2}}$, find the value of $\sqrt{{S}_{1}}+\sqrt{{S}_{2}}+\ldots+\sqrt{{S}_{24}}$.

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