
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 $\{a_n\}$ where $a_1=a$, $\{b_n\}$ is a geometric sequence with a common ratio of $\frac{2}{3}$. It is known that $b_n = \frac{a_n - 2}{a_n - 1}, n \in \mathbb{N}^*$. If the inequality $a_n > a_{n+1}$ holds for all $n \in \mathbb{N}^*$, determine the range of the real number $a$.

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