
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
For which values of \(a\) is the polynomial \(P(x)=a^{3} x^{5}+(1-a) x^{4}+\left(1+a^{3}\right) x^{2}+(1-3 a) x-a^{3}\) divisible by \(x-1\)?

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