
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
The function $f(x) = 3x^2 + 3x - 8$, in the process of calculating the root of $3x^2 + 3x - 8 = 0$ within $x \in (1, 2)$ using the bisection method, it is found that: $f(1) < 0$, $f(1.5) > 0$, $f(1.25) < 0$. Therefore, determine the interval where the root of the equation lies, in the interval $(1, 2)$.

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