
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 $f(x) = x^3 - 2x - 5$, and $f(2.5) > 0$, use the "bisection method" to find the real root of the equation $x^3 - 2x - 5 = 0$ within the interval $(2, 3)$. Taking the midpoint of the interval as $x = 2.5$, the next interval containing the root is ____.

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