
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 positive integer  $n$ , let  $a_n=\sum_{k=1}^{\infty}[\frac{n+2^{k-1}}{2^k}]$ , where  $[x]$  is the largest integer that is equal or less than  $x$ . Determine the value of  $a_{2015}$ .

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