
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 graph of $f(x)$ is continuous on the interval $[a, b]$ and $f(a)f(b) < 0$, when using the bisection method to find the root of the corresponding equation, if $f(a) < 0$, $f(b) > 0$, and $f(\frac{a+b}{2}) > 0$, then the interval with the root is $\_\_\_\_\_\_$.

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