
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 $f(x)=3^{x}$, where $f(a+2)=27$, and the function $g(x)=λ \cdot 2^{ax}-4^{x}$ with a domain of $[0,2]$, find:

(1) The value of $a$;
(2) The value of the real number $λ$ if the maximum value of function $g(x)$ is $\frac{1}{3}$.

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