
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
Use the bisection method to find the approximate root of the function $y=f(x)$ in the interval $[2,4]$. It has been verified that $f(2) \cdot f(4) < 0$. Taking the midpoint of the interval as $x_{1}=3$, it is calculated that $f(2) \cdot f(x_{1}) < 0$. At this time, the root $x_{0} \in$ _______; (Fill in the interval)

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