
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 $f(x)=ax^{3}- \frac {3}{2}x^{2}+1$ $(x\in\mathbb{R})$, where $a > 0$.  
$(1)$ If $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(2,f(2))$;  
$(2)$ If for $\forall x\in[-1, \frac {1}{2}]$, the inequality $f(x) < a^{2}$ always holds, find the range of values for $a$.

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