
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 $A=\{x|x^{2}-2x-3 < 0\}$, $B=\{x|2a-1 < x < a+1\}$, where $a \in \mathbb{R}$.  
(1) If "$x \in A$" is a necessary condition for "$x \in B$", find the range of the real number $a$;  
(2) Let the function $f(x)=a\sin(2x+ \frac{\pi}{3})+1$, if the real number $x_{0}$ satisfies $f(x_{0}) \in A$, find the set of values for the real number $x_{0}$.

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