
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
When studying the root of the function $f(x) = x^3 + 3x - 1$ using the bisection method, after the first calculation it is found that $f(0) < 0$ and $f(0.5) > 0$. Determine the interval containing one of the roots, $x_0$, and calculate the value of $f(0.25)$.

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