
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. The measures of the non-overlapping minor arcs $DE$, $EF$, and $FD$ are, respectively, $x+60^\circ$, $2x+40^\circ$, and $3x-12^\circ$. Find the measure of the interior angle at $D$.
A) $64^\circ$
B) $65^\circ$
C) $66^\circ$
D) $65.33^\circ$

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