
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 an approximate solution to $f(x) = 0$ accurate to within 0.1. Using a calculator, it is found that $f(2) < 0$, $f(3) > 0$, $f(2.5) < 0$, $f(2.75) > 0$, $f(2.625) > 0$, and $f(2.5625) > 0$. Determine the interval in which the approximate solution lies.

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