
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
Given the triangular pyramid $D-ABC$, where $\angle ACB=\angle ABD=90^{\circ}$, $CA=CB$, and $\angle BAD=30^{\circ}$. If the projection of point $C$ onto plane $ABD$ lies exactly on line $AD$, then find the sine of the dihedral angle between planes $CAB$ and $ABD$.

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