
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

Find two integers \( A \) and \( B \) that are 1 unit apart on the number line and possess the following property: a root of the equation \( x^{3}+5x^{2}-3x+1=0 \) lies in the interval \( (A, B) \).

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