
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 \( t = 2016 \) and \( p = \ln 2 \). Evaluate in closed form the sum
\[
\sum_{k=1}^{\infty}\left(1 - \sum_{n=0}^{k-1} \frac{e^{-t} t^n}{n!}\right)(1-p)^{k-1} p.
\]

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