
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
By studying the number of zeros of the function $f(x) = 2x^4 - 10x^2 + 2x - 1$ within $x \in \mathbb{R}$, further research on the function $g(x) = 2x^n + 10x^2 - 2x - 1$ ($n > 3$, $n \in \mathbb{N}$ and $n$ is odd) reveals that it has $\boxed{\text{3}}$ zeros within $x \in \mathbb{R}$.

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