
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 circle is centered at point \( O \) and is circumscribed around triangle \( DEF \) as shown:
- \( \angle DOE = 130^\circ \)
- \( \angle EOD = 90^\circ \)

What is the measure of \( \angle DEF \) and \( \angle EDF \), in degrees?

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