
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 $\triangle BAD$, we have a right-angle at $B$. A point $C$ is on segment $AD$ such that $AC = 2CD$ and $AB = 2BC$. Calculate the measure of $\angle DAB$.

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