
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  $P(x)=x^n+a_{n-1}x^{n-1}+\cdots+a_0$  be a polynomial of degree  $n\geq 3.$  Knowing that  $a_{n-1}=-\binom{n}{1}$  and  $a_{n-2}=\binom{n}{2},$  and that all the roots of  $P$  are real, find the remaining coefficients. Note that  $\binom{n}{r}=\frac{n!}{(n-r)!r!}.$ 

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