
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) Find the minimum value of the function $$f(x)= \frac {1}{\sin^{2}x}+ \frac {4}{\cos^{2}x}$$, where $$x \in (0, \frac {\pi}{2})$$.  
(2) Given that the solution set of the inequality $ax^2+bx+c>0$ is $(\alpha, \beta)$, and $0<\alpha<\beta$, express the solution set of the inequality $cx^2+bx+a<0$ in terms of $\alpha$ and $\beta$.

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