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

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