
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: ${e}^{ln3}-lo{g}_{\sqrt{2}}(2\sqrt{2})+(0.125)^{\frac{2}{3}}+\sqrt[2023]{(-2)^{2023}}$;<br/>$(2)$ Given $a^{2x}=2$, find the value of $\frac{a^{3x}+a^{-3x}}{a^{x}+a^{-x}}$.

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