
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
Consider the following expressions: $S_{1}=\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}=1+\frac{1}{1×2}$, $S_{2}=\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}=1+\frac{1}{2×3}$, $S_{3}=\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}=1+\frac{1}{3×4} \ldots $ Please calculate $S_{1}+S_{2}+\ldots +S_{50}=\_\_\_\_\_\_$ using the pattern you discovered.

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