
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 that \( p(x) \) is a 5th-degree polynomial, and \( x=0 \) is a triple root of \( p(x) + 1 = 0 \), and \( x=1 \) is a triple root of \( p(x) - 1 = 0 \), find the expression for \( p(x) \).

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