
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
Find all reals  $a$  such that the sequence  $\{x(n)\}$ ,  $n=0,1,2, \ldots$   that satisfy:  $x(0)=1996$  and  $x_{n+1} = \frac{a}{1+x(n)^2}$  for any natural number  $n$  has a limit as n goes to infinity.

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