
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 the function $f(x) = x^5 + 8x^3 - 1$, investigate the zero of the function using the bisection method. If it is found that $f(0) < 0$ and $f(0.5) > 0$, determine the interval containing a zero and the function value to be calculated in the second step.

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