
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 following expressions:  
(1) $$\frac {a^{2}}{ \sqrt {a}\cdot 3a^{2} }$$ (where the letter represents a positive number);  
(2) Calculate $$\frac {2\lg2+\lg3}{1+ \frac {1}{2}\lg0.36+ \frac {1}{3}\lg8}$$.

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