
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
Given a sequence $\{a_n\}$ with the general term $a_n=\log_{(n+1)}(n+2)$, $(n\in\mathbb{N}^*)$, we call $n$ a "prime number" if the product $a_1a_2a_3…a_n$ is an integer. Find the sum of all "prime numbers" in the interval $(1,2016]$.

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