
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
$(1)$ Given $x^{n}=2$, find the value of $(3x^{n})^{2}-4(x^{2})^{n}$;<br/>$(2)$ Given $x=2^{n}-1$ and $y=3+8^{n}$, express $y$ in terms of $x$.

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