
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 has one side measuring $10$ inches and the angle opposite this side is $45^\circ$. Determine the diameter of the circumscribed circle.
**A)** $10\text{ inches}$  
**B)** $15\text{ inches}$  
**C)** $20\text{ inches}$  
**D)** $10\sqrt{2} \text{ inches}$  
**E)** $20\sqrt{2} \text{ inches}$

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