
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 matrix operation $\left(\begin{array}{l}a&b\\ c&d\end{array}\right)\left(\begin{array}{l}x\\ y\end{array}\right)=\left(\begin{array}{l}ax+by\\ cx+dy\end{array}\right)$, evaluate $\left(\begin{array}{c}\log_{2}^{\frac{1}{4}}&\log_{2}25\\ \log_{2}5&\log_{2}256\end{array}\right)\left(\begin{array}{c}{8}^{\frac{2}{3}}\\{2}^{-1}\end{array}\right)$.

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