
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
For any real number $x$, $[x]$ denotes the largest integer not greater than $x$. Observe the following equations:
$$[ \sqrt {1}]+[ \sqrt {2}]+[ \sqrt {3}]=3$$
$$[ \sqrt {4}]+[ \sqrt {5}]+[ \sqrt {6}]+[ \sqrt {7}]+[ \sqrt {8}]=10$$
$$[ \sqrt {9}]+[ \sqrt {10}]+[ \sqrt {11}]+[ \sqrt {12}]+[ \sqrt {13}]+[ \sqrt {14}]+[ \sqrt {15}]=21$$
$$\vdots$$
According to this pattern, the result on the right side of the equal sign in the $n$th equation is $\_\_\_\_\_\_$.

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