
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 $A=\{x\mid 2\leqslant x < 7\}$, $B=\{x\mid 3 < x\leqslant 10\}$, and $C=\{x\mid a-5 < x < a\}$.
1. Find $A\cap B$ and $A\cup B$.
2. If the non-empty set $C$ is a subset of $A\cup B$, find the range of values for $a$.

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