
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 two sets, $A = \{x \mid 0 < ax+1 \leq 5\}$ and $B = \{x \mid -\frac{1}{2} < x \leq 2\}$,

(1) Determine if $B \subseteq A$ holds when $a=1$.

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

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