
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 the function $f(x) = 3x^2 - 1$ has a unique zero point $x_0$ in the interval $(0, 1)$. If the "bisection method" is used to approximate this zero point with an accuracy of $\epsilon = 0.05$, then the minimum number of times the interval $(0, 1)$ needs to be equally divided is \_\_\_\_\_\_, and it is stipulated that as long as the existence interval $(a, b)$ of the zero point satisfies $|a-b| < \epsilon$, then $\frac{a+b}{2}$ is used as the approximate value of the zero point. Thus, the obtained $x_0$ is \_\_\_\_\_\_.

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