
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 $$f(x)= \frac {x^{3}}{a^{2}}$$, the distance between two tangent lines with a slope of 3 on its graph is $$\frac {2 \sqrt {10}}{5}$$. The function $$g(x)=f(x)- \frac {3bx}{a^{2}}+3$$.
(1) If the function $g(x)$ has an extremum at $x=1$, find the expression for $g(x)$;
(2) If the function $g(x)$ is increasing on the interval \[-1, 1\], and $b^2-mb+4 \geq g(x)$ holds true for $x \in [-1, 1]$, find the range of the real number $m$.

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