
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 $[x]$ represent the greatest integer less than or equal to $x$. Given that the natural number $n$ satisfies $\left[\frac{1}{15}\right] + \left[\frac{2}{15}\right] + \left[\frac{3}{15}\right] + \cdots + \left[\frac{n-1}{15}\right] + \left[\frac{n}{15}\right] > 2011$, what is the smallest value of $n$?

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