
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
Compute
\[
\begin{vmatrix} \sin 30^\circ & \sin 60^\circ & \sin 90^\circ \\ \sin 150^\circ & \sin 180^\circ & \sin 210^\circ \\ \sin 270^\circ & \sin 300^\circ & \sin 330^\circ \end{vmatrix}
.\] All the angles are in degrees.

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