
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
Simplify and evaluate:  
(1) $(2a^{ \frac {2}{3}}b^{ \frac {1}{2}})(-6a^{ \frac {1}{2}}b^{ \frac {1}{3}})÷(-3a^{ \frac {1}{6}}b^{ \frac {5}{6}})$;  
(2) $(\lg2)^2+\lg2\cdot\lg5+ \sqrt {(\lg2)^{2}-2\lg2+1}$.

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