
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)=3^{x}+3x-8\\), when using the bisection method to find an approximate solution of the equation \\(3^{x}+3x-8=0\\) within \\(x∈(1,2)\\), it was found that \\(f(1) < 0\\), \\(f(1.5) > 0\\), and \\(f(1.25) < 0\\). Determine the interval within which the root of the equation lies.

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