
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 and evaluate:
$(1)(2 \frac{7}{9})^{0.5}+0.1^{-2}-\pi^{0}+\frac{1}{3};$
$(2)((xy^{2} \cdot x^{\frac{1}{2}} \cdot y^{-\frac{1}{2}})^{\frac{1}{3}} \cdot (xy)^{\frac{1}{2}})$, where $x > 0$, $y > 0$.

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