
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:<br/>$(1)$ Given $2\cdot 8^{n}\cdot 32^{n}=2^{17}$, find the value of $n$;<br/>$(2)$ If $n$ is a positive integer and $x^{2n}=2$, find the value of $(2x^{3n})^{2}-3(x^{2})^{2n}$.

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