
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
The function $\[x\]$ represents the largest integer not greater than $x$. For example, $\[π\]=3$. Let $S\_1=\[√1\}+\[√2\}+\[√3\}=3$, $S\_2=\[√4\}+\[√5\}+\[√6\}+\[√7\}+\[√8\}=10$, and $S\_3=\[√9\}+\[√10\}+\[√11\}+\[√12\}+\[√13\}+\[√14\}+\[√15\}=21$. Following this pattern, find $S\_{10}=$\_\_\_\_\_\_\_\_.

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