
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:  
(1) $$\sqrt {32} - 4 \sqrt {0.5} + 3 \sqrt {8}$$;  
(2) $$\frac {1}{2} (\sqrt {3} + \sqrt {2}) - \frac {3}{4} (\sqrt {2} - \sqrt {27})$$.

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