
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 operation $$\begin{bmatrix} \left.\begin{matrix}a & b \\ c & d\end{matrix}\right.\end{bmatrix}$$• $$\begin{bmatrix} \left.\begin{matrix}e \\ f\end{matrix}\right.\end{bmatrix}$$ = $$\begin{bmatrix} \left.\begin{matrix}ae+ & bf \\ ce+ & df\end{matrix}\right.\end{bmatrix}$$, such as $$\begin{bmatrix} \left.\begin{matrix}1 & 2 \\ 0 & 3\end{matrix}\right.\end{bmatrix}$$• $$\begin{bmatrix} \left.\begin{matrix}4 \\ 5\end{matrix}\right.\end{bmatrix}$$ = $$\begin{bmatrix} \left.\begin{matrix}14 \\ 15\end{matrix}\right.\end{bmatrix}$$. Given α+β=π and α-β= $$\frac {π}{2}$$, then $$\begin{bmatrix} \left.\begin{matrix}sinα & cosα \\ cosα & sinα\end{matrix}\right.\end{bmatrix}$$• $$\begin{bmatrix} \left.\begin{matrix}cosβ \\ sinβ\end{matrix}\right.\end{bmatrix}$$ = \_\_\_\_\_\_ .

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