
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 $S_n = \left\lfloor \log_2 1 \right\rfloor + \left\lfloor \log_2 2 \right\rfloor + \left\lfloor \log_2 3 \right\rfloor + \ldots + \left\lfloor \log_2 n \right\rfloor$ (where $\left\lfloor x \right\rfloor$ denotes the greatest integer less than or equal to $x$, e.g., $\left\lfloor 0.9 \right\rfloor = 0$, $\left\lfloor 2.6 \right\rfloor = 2$), then find the value of $S_{2017}$.

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