
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
Compute the following expressions:
1. $(1)(1+ \sqrt {3})(2- \sqrt {3})$
2. $(2)( \sqrt { \frac {9}{2}}- \frac { \sqrt {8}}{3}) \times 2 \sqrt {2}$
3. $\sqrt {18}- \sqrt {8}+ \sqrt { \frac {1}{8}}$
4. $( \sqrt {6}-2 \sqrt {15}) \times \sqrt {3}-6 \sqrt { \frac {1}{2}}$

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