
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 $A=\{x\in\mathbb{R}|0<ax+1\leq5\}$ and $B=\{x\in\mathbb{R}|-\frac{1}{2}<x\leq2\}$.

(1) Can sets $A$ and $B$ be equal? If yes, determine the value of the real number $a$. If not, explain the reason.

(2) Let proposition $p$ be 'x belongs to set $A$' and proposition $q$ be 'x belongs to set $B$' and $p$ is a sufficient but not necessary condition for $q$. Determine the range of values for the real number $a$.

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