
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
A triangle $\triangle DEF$ is inscribed in a circle of radius $r$ such that its side $DE$ is the diameter of the circle. Point $F$ lies on the circle but is not coincident with points $D$ or $E$. Let $t = DF + EF$. Determine the maximum value of $t^2$ in terms of $r$.

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