
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 that sets A and B are subsets of the real numbers R, define A-B={x|x∈A, and x∉B}, and the symmetric difference of the sets A*B=(A-B)∪(B-A). If set A={y|y=(x-1)²+1, 0≤x≤3}, and B={y|y=x²+1, 1≤x≤3}, find A*B.

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