
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 $f(x) = ax^2 - 4x + 2$, and the function $g(x) = \left(\frac{1}{3}\right)^{f(x)}$  
(Ⅰ) If the axis of symmetry of $y=f(x)$ is $x=2$, find the expression for $f(x)$;  
(Ⅱ) Under the condition of (Ⅰ), find the range of $g(x)$.

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