
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 equation $3^x + 3x - 8 = 0$, in the process of using the bisection method to find an approximate solution within the interval $x \in (1, 2)$, $f(2) > 0$, $f(1.5) < 0$, and $f(1.75) > 0$. Determine the interval in which the root of the equation appears.

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