
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 universal set $U=\mathbb{R}$, and the sets $A=\{x\mid -1 < x < 3\}$, $B=\{x\mid 0 < x\leqslant 4\}$, $C=\{x\mid a < x < a+1\}$.

1. Find $A\cup B$ and $(A^c\cap B^c)$;
2. 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}
user