
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 value of the following expression:
$(1)(2\frac{7}{9})^{\frac{1}{2}} - (2\sqrt{3} - \pi)^{0} - (2\frac{10}{27})^{-\frac{2}{3}} + 0.25^{-\frac{3}{2}}$
2. Given that $x + x^{-1} = 4 (0 < x < 1)$, find the value of ${x^{\frac{1}{2}}} + {x^{-\frac{1}{2}}}$.

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