
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 $[x]$ denote the greatest integer less than or equal to x, for example, $[\pi] = 3$. Consider the following sums:
$S_1 =[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}] = 3$,
$S_2 =[\sqrt{4}]+[\sqrt{5}]+[\sqrt{6}]+[\sqrt{7}]+[\sqrt{8}] = 10$,
$S_3 =[\sqrt{9}]+[\sqrt{10}]+[\sqrt{11}]+[\sqrt{12}]+[\sqrt{13}]+[\sqrt{14}]+[\sqrt{15}] = 21$, ...
Following this pattern, find the value of $S_{10}$.

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