
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
Calculate: ${(\frac{81}{16})}^{-\frac{1}{4}}+\frac{1}{4}\log_{\sqrt{2}}3\times\log_{3}4\times{[(-\frac{1}{3})}^{2]}^{\frac{1}{2}}+{7}^{\log_{7}\frac{1}{2}}$.

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