
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 a diagram, triangles ABC and ABD share side AB, with vertices C and D lying in opposite directions from B along different lines. Triangle ABC is a right triangle with a right angle at C, and ∠CAB = 45°. Triangle ABD is a right triangle with a right angle at D, and ∠DAB = 30°. If CD has a length of 6 units, find the length of line segment AB.

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