
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 $f(x) = 3^x$, and $f(a+2) = 18$, let the function $g(x) = \lambda \cdot 3^{ax} - 4^x$ have the domain $[0, 1]$.
(Ⅰ) Find the value of $a$.
(Ⅱ) If the function $g(x)$ is a monotonically decreasing function on the interval $[0, 1]$, determine the range of values for the real number $\lambda$.

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