
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
Find the value of $n$ in the following equations.<br/>$(1)A_{2n}^3=2A_{n+1}^4$;<br/>$(2)C_{n+2}^{n-2}+C_{n+2}^{n-3}=\frac{1}{{10}}A_{n+3}^3$.

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