
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 \( k \geqslant 0 \), determine the minimum of the expression 
\[ A=\frac{x}{1+y^{2}}+\frac{y}{1+x^{2}}+\frac{z}{1+t^{2}}+ \frac{t}{1+z^{2}} \]
under the condition \( x + y + z + t = k \) and \( x, y, z, t \) are positive.

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