
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
Among the following equations, the valid ones are __________. (Fill in the serial numbers)

1. $C_n^m= \frac{A_n^m}{m!}$;

2. $C_n^m=C_n^{n-m}$;

3. $C_{n+1}^r=C_n^r+C_n^{r-1}$;

4. $A_{n+2}^{m+2}=(n+2)(n+1)A_n^m$.

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