
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
Try to solve the following problems related to powers.  
$(1)$ If $9 \times 27^{x} = 3^{17}$, find the value of $x$.  
$(2)$ Given $a^{x} = -2$, $a^{y} = 3$, find the value of $a^{3x-2y}$.

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