
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 the convex quadrilateral \(ABCD\), diagonals \(AC\) and \(BD\) intersect at point \(P\). Given that \(\angle DBC = 60^{\circ}\), \(\angle ACB = 50^{\circ}\), \(\angle ABD = 20^{\circ}\), and \(\angle ACD = 30^{\circ}\), find the measure of \(\angle ADB\).

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