
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
Find the angles of the convex quadrilateral \(ABCD\) given that \(\angle BAC = 30^\circ\), \(\angle ACD = 40^\circ\), \(\angle ADB = 50^\circ\), \(\angle CBD = 60^\circ\), and \(\angle ABC + \angle ADC = 180^\circ\).

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