
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
Investigate the zero of the function $f(x) = x^3 + 3x - 1$ using bisection method. After the first calculation, we find that $f(0) < 0$ and $f(0.5) > 0$, which means one of the zeros $x$ is in the interval $(0, 0.5)$. For the second calculation, we should compute $f(0.25)$. Determine the new interval that contains $x$.

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