
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
Given a convex quadrilateral \(ABCD\) with \(\angle C = 57^{\circ}\), \(\sin \angle A + \sin \angle B = \sqrt{2}\), and \(\cos \angle A + \cos \angle B = 2 - \sqrt{2}\), find the measure of angle \(D\) in degrees.

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