
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 that $a_n = \log_{n+1}(n+2)$ for $n \in \mathbb{N}^*$, consider the following expressions: $(a_1a_2 = \log_2 3 \cdot \log_3 4 = \frac{\lg 3}{\lg 2} \cdot \frac{\lg 4}{\lg 3} = 2)$ and $(a_1a_2a_3a_4a_5a_6 = \log_2 3 \cdot \log_3 4 \cdot \dots \cdot \log_7 8 = \frac{\lg 3}{\lg 2} \cdot \frac{\lg 4}{\lg 3} \cdot \dots \cdot \frac{\lg 8}{\lg 7} = 3)$. If $a_1a_2 \dots a_m = 2016$ for $m \in \mathbb{N}^*$, then the value of $m$ is
A) $2^{2016} + 2$
B) $2^{2016}$
C) $2^{2016} - 2$
D) $2^{2016} - 4$

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