
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
If $C_{23}^{3n+1}=C_{23}^{n+6}$ $(n\in{N}^{*})$ and $(3-x)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+\cdots+a_{n}x^{n}$, then $a_{0}-a_{1}+a_{2}-\cdots+(-1)^{n}a_{n}=$ _________

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