
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
(1) Given the function $f(x)=(\frac{1}{3})^{x}$

(1) If $y=f(x)$ and $y=f^{-1}(x)$ are inverse functions, find the monotonic intervals of $g(x)=f^{-1}(x^{2}+2x-3)$.

(2) When $x \in [-1,1]$, find the maximum and minimum values of $y=[f(x)]^{2}-2f(x)+3$.

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