
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: ${(\frac{27}{8})}^{-\frac{2}{3}}+{π}^{lg1}+log_{2}\frac{2}{3}-log_{4}\frac{16}{9}$;  
$(2)$ Given ${a}^{\frac{1}{2}}+{a}^{-\frac{1}{2}}=3$, find the value of $\frac{{a}^{3}+{a}^{-3}}{a+{a}^{-1}}$.

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