
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
(1) Calculate the expression $\sqrt {5}-( \sqrt {3}+ \sqrt {15})÷ \sqrt {6}× \sqrt {2}$.
(2) Calculate the expression $( \sqrt {48}-4 \sqrt { \frac {1}{8}})-(3 \sqrt { \frac {1}{3}}-2 \sqrt {0.5})$.
(3) Calculate the expression $(3+ \sqrt {5})(3- \sqrt {5})-( \sqrt {3}-1)^{2}$.
(4) Calculate the expression $(- \sqrt {3}+1)( \sqrt {3}-1)- \sqrt {(-3)^{2}}+ \frac {1}{2- \sqrt {5}}$.

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