
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 $f(x)=\lg [(2x-3)(x- \frac {1}{2})]$ with domain set $A$, and function $g(x)= \sqrt {-x^{2}+4ax-3a^{2}}$ (where $a > 0$) with domain set $B$.

1. Find the set $A∩B$ when $a=1$.
2. If $A∩B=B$, find the range of values for the real number $a$.

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