
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 determinant $$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$$ as $ad - bc$. Compute the sum of the determinants: $$\begin{vmatrix} 2 & 4 \\ 6 & 8 \end{vmatrix} + \begin{vmatrix} 10 & 12 \\ 14 & 16 \end{vmatrix} + \ldots + \begin{vmatrix} 2010 & 2012 \\ 2014 & 2016 \end{vmatrix} = \_\_\_\_\_\_.$$

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