
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 two triangles, $\triangle ABC$ and $\triangle DEF$, with sides $ABC$ having side lengths 9, 40, and 41, and $DEF$ having side lengths 13, 84, and 85. Verify if both triangles are right triangles and if so, determine whether a circle with a diameter equal to the longest side of each triangle can encircle both triangles.
A) 41, 85
B) 41, 84
C) 40, 85
D) 9, 13

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