
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: (1) $\frac{1}{3}\sqrt{36}-2\sqrt[3]{125}-\sqrt{(-4)^{2}}$. (2) $(\sqrt{8}-\sqrt{\frac{2}{3}})-(6\sqrt{\frac{1}{2}}+\sqrt{24})$. (3) $(\sqrt{6}-2\sqrt{3})^2+\sqrt{27}(\sqrt{54}-\sqrt{12})$.

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