
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
 $ABCD$  is circumscribed in a circle  $k$ , such that  $[ACB]=s$ ,  $[ACD]=t$ ,  $s<t$ . Determine the smallest value of  $\frac{4s^2+t^2}{5st}$  and when this minimum is achieved.

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