
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 operation $$\begin{bmatrix} a & b \\ c & d\end{bmatrix}$$• $$\begin{bmatrix} e \\ f\end{bmatrix}$$= $$\begin{bmatrix} ae+bf \\ ce+df\end{bmatrix}$$ and that α+β=π and α-β= $$\frac {π}{2}$$, find the result of $$\begin{bmatrix} \sinα & \cosα \\ \cosα & \sinα\end{bmatrix}$$• $$\begin{bmatrix} \cosβ \\ \sinβ\end{bmatrix}$$.

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