
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: $\frac{{A}_{5}^{2}+{C}_{5}^{2}}{{A}_{3}^{3}-{A}_{4}^{2}}$;  
$(2)$ Given $C_{17}^{3x}=C_{17}^{2x+2}$ ($x\in\mathbb{N}^*$), find $x$.

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