
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 $S_{n}=[\log_{2}1]+[\log_{2}2]+[\log_{2}3]+…+[\log_{2}n]$, where $[x]$ denotes the largest integer not greater than $x$ (e.g., $[0.9]=0$, $[2.6]=2$). Determine the value of $S_{2017}$.

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