
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. Given that $x > 0$, $y > 0$, and they satisfy $\frac{2}{x}+\frac{8}{y}=1$, find the minimum value of $x+y$.
2. Points $A$ and $B$ are 2 kilometers apart, and the angles $∠CAB=75^{\circ}$, $∠CBA=60^{\circ}$. Find the distance between points $A$ and $C$.
3. In a geometric sequence ${a_n}$, all terms are positive, and $a_{1}a_{5}=4$. Find the value of $\log _{2}a_{1}+\log _{2}a_{2}+\log _{2}a_{3}+\log _{2}a_{4}+\log _{2}a_{5}$.
4. The sum of the first $n$ terms of the sequence ${a_n}$ is $S_{n}$, $a_{1}=1$, $a_{n+1}=2S_{n}$ $(n∈N^{+})$. Find the general term $a_{n}$ of the sequence ${a_n}$.

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