
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 the domain of the function $f(x)=\sqrt{(1+x)(2-x)}$ is set $A$, and the domain of the function $g(x)=\ln(x-a)$ is set $B$.

(1) Find sets $A$ and $B$;

(2) If $C=\{x\mid 2^{x^{2}-2x-3} < 1\}$, find $A\cap C$.

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