
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
$\triangle DEF$ is inscribed in a circle of radius $r$ with its base $DE$ coinciding with the diameter of the circle. Point $F$ is any point on the circumference that is not coincidental with points $D$ or $E$. Let $t = DF + EF$. Find the maximum value of $t^2$ given that the circle is of radius $r$.

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