
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
The sequence $\{a_n\}$ satisfies: $a_1=2$, $a_{n+1}=a_1+a_2+\ldots+a_n+6$, ($n\in\mathbb{N}^*$).
1. Determine whether $\{a_n\}$ is a geometric sequence and explain the reason.
2. Let $b_n=\log_2 a_n$, if $x < \frac{1}{b_1b_2} + \frac{1}{b_2b_3} + \ldots + \frac{1}{b_nb_{n+1}} < y$ holds for all $n\in\mathbb{N}^*$, find the range of values for $x$ and $y$.

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