
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
For the curve  $ C: y = \frac {1}{1 + x^2}$ , Let  $ A(\alpha ,\ f(\alpha)),\ B\left( - \frac {1}{\alpha},\ f\left( - \frac {1}{\alpha} \right)\right)\ (\alpha > 0).$  Find the minimum area bounded by the line segments  $ OA,\ OB$  and  $ C,$  where  $ O$  is the origin.

Note that you are not allowed to use the integral formula of  $ \frac {1}{1 + x^2}$  for the problem.

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