
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 the function $f(x) = \log_a(x-b)$ (where $a$ and $b$ are constants, $a>0$ and $a \neq 1$) passes through two points $M(3, 0)$ and $N(6, 1)$.
(Ⅰ) Determine the explicit formula of function $f(x)$;
(Ⅱ) If the function $g(x) = \left(\frac{a}{b}\right)^{2x} - 6\left(\frac{a}{b}\right)^{x} + 5$, where $x \in [1, 3]$, find the range of $g(x)$.

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