
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 that $a > 0$, the functions are defined as $f(x)=a^{2}x^{3}-3ax^{2}+2$ and $g(x)=-3ax+3$.
(1) If $a=1$, find the equation of the tangent line to the graph of function $f(x)$ at the point where $x=1$;
(2) Find the extreme values of function $f(x)$ in the interval $[-1,1]$;
(3) If there exists $x_{0} \in (0, \frac{1}{2}]$ such that the inequality $f(x_{0}) > g(x_{0})$ holds, find the range of values for $a$.

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