
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
Suppose in a quadrilateral ABCD, where $\angle A$ and $\angle D$ are opposite angles, it is given that $\angle A = 105^\circ$ and $\angle B = \angle C$. Also, $\angle A + \angle B + \angle C + \angle D = 360^\circ$. Find the measure of $\angle D$.

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