
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 $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$, for example, $\lfloor \pi \rfloor = 3$.  
$S_{1}=\lfloor \sqrt {1} \rfloor+\lfloor \sqrt {2} \rfloor+\lfloor \sqrt {3} \rfloor=3$  
$S_{2}=\lfloor \sqrt {4} \rfloor+\lfloor \sqrt {5} \rfloor+\lfloor \sqrt {6} \rfloor+\lfloor \sqrt {7} \rfloor+\lfloor \sqrt {8} \rfloor=10$  
$S_{3}=\lfloor \sqrt {9} \rfloor+\lfloor \sqrt {10} \rfloor+\lfloor \sqrt {11} \rfloor+\lfloor \sqrt {12} \rfloor+\lfloor \sqrt {13} \rfloor+\lfloor \sqrt {14} \rfloor+\lfloor \sqrt {15} \rfloor=21$，...  
Following this pattern, then $S_{10}=$ ______.

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