
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 $$f(x)=( \frac {1}{3})^{x}$$.
(1) If $g(x)$ is the inverse function of $f(x)$, and the domain of $g(mx^2+2x+1)$ is $\mathbb{R}$, find the range of the real number $m$;
(2) When $x \in [-1, 1]$, find the minimum value $g(a)$ of the function $y=[f(x)]^2-2af(x)+3$.

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