
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\} satisfying $a_1 = 1$ and $a_n = \log_n (n+1)$ for $n \geq 2$ and $n \in \mathbb{N}^*$. Define: $k \in \mathbb{N}^*$ that makes the product $a_1 \times a_2 \times \ldots \times a_k$ a positive integer to be called "easy integer". Find the sum of all "easy integers" in the interval [1, 2015].

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