
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) = lg x + x - 3, apply the bisection method to find an approximate root of the equation ln x + x - 3 = 0 within the interval (2,3). During the process, it is found that f(2.25) < 0, f(2.75) > 0, f(2.5) < 0, and f(3) > 0. Determine the interval in which the root of the equation lies.

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