
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
For any positive integer \( n \), let the functions \( f_{n}: \mathbb{R} \rightarrow \mathbb{R} \) be defined by \( f_{n+1}(x)=f_{1}\left(f_{n}(x)\right) \), where \( f_{1}(x)=3x-4x^{3} \). Solve the equation \( f_{n}(x)=0 \).

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