
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 $A=\{x\mid \frac{2-x}{3+x}\geqslant 0\}$, $B=\{x\mid x^{2}-2x-3 < 0\}$, and $C=\{x\mid x^{2}-(2a+1)x+a(a+1) < 0\}$.

(I) Find the sets $A$, $B$, and $A\cup B$;

(II) If $C\subseteq(A\cap B)$, find the range of values for the real number $a$.

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