
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  $p$  be a monic cubic polynomial such that  $p(0)=1$  and such that all the zeroes of  $p^\prime (x)$  are also zeroes of  $p(x)$ .  Find  $p$ .  Note: monic means that the leading coefficient is  $1$ .

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