
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 following:
(1) Find the value: $27^{\frac{2}{3}} - (\sqrt[3]{-125})^2 - 2^{\log_{2}3} \times \log_{2}\frac{1}{8} + \log_{2}3 \times \log_{3}4$.
(2) Find the solution set of the inequality: ① $3^{3-x} < 2$; ② $\log_{5}(x-1) < \frac{1}{2}$.

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