
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 the lowest-degree polynomial \( p(x) \) that satisfies the following conditions:
a) The coefficients of \( p(x) \) are integers,
b) \( p(x) \) can be factored into a product of first-degree polynomials,
c) The roots of \( p(x) \) are integers,
d) \( p(0) = -1 \),
e) \( p(3) = 128 \).

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