
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 $f(x)= \frac {x+2-kx^{2}}{x^{2}}$ and the solution set for $f(x) > 0$ is $(-1,0)∪(0,2)$.

1. Find the value of $k$.
2. If the real number $t$ simultaneously satisfies the following two propositions:
   1. $∀x∈( \frac {1}{2},1)$, $t-1 < f(x)$ always holds.
   2. $∃x_{0}∈(-5,0)$, $t-1 < f(x_{0})$ holds. Find the range of values for the real number $t$.
3. If the equation concerning $x$, $\ln f(x)+2\ln x=\ln (3-ax)$, has only one solution, find the range of values for the real number $a$.

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