
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 the value of the following expressions:
1. ($\frac{27}{8})^{\frac{2}{3}}$ + ($\frac{1}{5})^{-\frac{1}{2}}$ + $\sqrt{(\sqrt{5} - 3)^2}$;
2. $\log_3{\frac{2}{3}}$ - $\log_3{\frac{2}{9}}$ - $\log_2{3} \cdot \log_9{4}$.

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