
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 sets $$A=\{x| \frac {1}{2}＜2^{x}＜4\}$$, B={x|x＜a}, C={x|m-1＜x＜2m+1},  
(1) Find the set A, and determine the range of the real number a when A⊆B;  
(2) If A∪C=A, find the range of the real number m;  
(3) Find the range of the function $y=4^{x}-2^{x+1}-1$ when $x\in A$.

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