
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 set $A=\{t|\text{The range of the function } f(x)=\lg[(t+2)x^2+2x+1] \text{ is } \mathbb{R}\}$, $B=\{x|(ax-1)(x+a)>0\}$  
(1) Find the set $A$;  
(2) If $A \subseteq B$, find the range of the real number $a$.

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