
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
In circle $\omega$, triangle $DEF$ is inscribed. The measures of the non-overlapping minor arcs $DE$, $EF$, and $FD$ are respectively $x + 90^\circ$, $2x + 50^\circ$, and $3x - 40^\circ$. Determine the measure of interior angle $D$.
A) $66^{\circ}$
B) $67^{\circ}$
C) $68^{\circ}$
D) $69^{\circ}$

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