
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
Let  $ t$  be a positive number. Draw two tangent lines from the point  $ (t, \minus{} 1)$  to the parabpla  $ y \equal{} x^2$ . Denote  $ S(t)$  the area bounded by the tangents line and the parabola. Find the minimum value of  $ \frac {S(t)}{\sqrt {t}}$ .

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