
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) Solve the inequality $\log_{\frac{1}{2}}(x+2) > -3$.  
(2) Calculate: $\left(\frac{1}{8}\right)^{\frac{1}{3}} \times \left(-\frac{7}{6}\right)^0 + 8^{0.25} \times \sqrt[4]{2} + \left(\sqrt[3]{2} \times \sqrt{3}\right)^6$.

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