
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 $A={x|x^2-2x+2a-a^2\leqslant 0}$ and $B={x|\sin (πx- \frac {π}{3})+ \sqrt {3}\cos (πx- \frac {π}{3})=0}$.
1. If $2\in A$, find the range of values for $a$.
2. If $A\cap B$ has exactly $3$ elements, find the range of values for $a$.

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