
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
Define the second-order determinant $$\begin{vmatrix} a & b \\ d & c \end{vmatrix} = ac - bd,$$ then calculate $$\begin{vmatrix} \sin50° & \cos40° \\ -\sqrt{3}\tan10° & 1 \end{vmatrix}.$$

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