
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) $\sqrt{\dfrac{2}{3}}-\left(\dfrac{1}{6}\sqrt{24}-\dfrac{3}{2}\sqrt{12}\right)$

(2) $\sqrt{12}+\left(\dfrac{1}{3}\right)^{-1}+|\sqrt{3}-1|-\left(\pi -2\right)^{0}$.

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