
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
[asy] draw((0,0)--(3,3)--(4,1)--(3,0)--cycle,dot); MP("A",(0,0),W);MP("B",(3,3),N);MP("C",(4,1),SE);MP("D",(3,0),S); MP("a",(1.5,0),N);MP("b",(3.5,2),N); [/asy]
In the diagram, segments $AB$ and $CD$ are parallel, the measure of angle $D$ is thrice that of angle $B$, and the measures of segments $AD$ and $CD$ are $a$ and $b$ respectively. Then the measure of $AB$ is equal to?

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