
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 a set $A$ whose elements are all real numbers, and it satisfies: if $a \in A$, then $\frac{1+a}{1-a} \in A$.
(1) If $a = -3$, find all other elements in $A$;
(2) Is $0$ an element of set $A$? Please design a real number $a \in A$, and then find all elements in $A$;
(3) Based on (1) and (2), what conclusion can you draw?

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