
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
Let \( f(x)=3^{x}+3x-8 \). Use the bisection method to find an approximate solution of the equation \( 3^{x}+3x-8=0 \) in the interval \( x∈(1,2) \). During the process, it is given that \( f(1) < 0 \), \( f(1.25) < 0 \), \( f(1.5) > 0 \). Therefore, the root of the equation falls within the interval \( ( \ ) \).

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