
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
Find the value of the following expressions:
\\[(1) \frac{(a^{\frac{2}{3}} \cdot b^{-1})^{-\frac{1}{2}} \cdot a^{\frac{1}{2}} \cdot b^{\frac{1}{3}}}{\sqrt[6]{a \cdot b^{5}}} \ (a > 0, b > 0)\\]
\\[(2) \frac{1}{2} \lg \frac{32}{49} - \frac{4}{3} \lg \sqrt{8} + \lg \sqrt{245}\\\]

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