
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 the function $f(x) = C_{n}^{0}x^{2n-1} - C_{n}^{1}x^{2n} + C_{n}^{2}x^{2n+1} - \ldots + C_{n}^{r}(-1)^{r} \cdot x^{2n-1+r} + \ldots + C_{n}^{n}(-1)^{n} \cdot x^{3n-1}$, where $n \in \mathbb{N}^{*}$, then $f'(1) = \_\_\_\_\_\_$.

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