
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 a quadratic equation $ax^2+bx+c=0$ with two real roots, let the sum of the roots be $s_1$, the sum of their squares be $s_2$, and the sum of their cubes be $s_3$. Find the value of $as_3+bs_2+cs_1$.

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