
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
Given that $\binom{23}{3n+1} = \binom{23}{n+6}$ where $n \in \mathbb{N}^*$ and $(3-x)^{n} = a_{0} + a_{1}x + a_{2}x^{2} + \dots + a_{n}x^{n}$, find the value of $a_{0} - a_{1} + a_{2} - \dots + (-1)^{n}a_{n}$.

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