
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
Let $S_1=1+\frac{1}{1^2}+\frac{1}{2^2}$, $S_2=1+\frac{1}{2^2}+\frac{1}{3^2}$, $S_3=1+\frac{1}{3^2}+\frac{1}{4^2}$, $\ldots$, $S_n=1+\frac{1}{n^2}+\frac{1}{(n+1)^2}$. Find the value of $\sqrt{{S}_{1}}+\sqrt{{S}_{2}}+…+\sqrt{{S}_{14}}$.

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