
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 p: A={x|a+1≤x≤2a-1}, B={x|x≤3 or x>5}, A⊆B; q: The function f(x)=x^2-2ax+1 is increasing on (1/2,+∞). If "p∧q" is false, and "p∨q" is true, find the range of values for the real number a.

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