
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 the following expressions:

$(1)$ $(0.027)^{\frac{2}{3}}+\left(\frac{27}{125}\right)^{-\frac{1}{3}}-\left(2\frac{7}{9}\right)^{0.5}$;

$(2)$ $(\log_{3}2+\log_{9}2)\cdot(\log_{4}3+\log_{8}3)$.

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