
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  $100$  quadratic polynomials  $f_1(x)=ax^2+bx+c_1, ... f_{100}(x)=ax^2+bx+c_{100}$ . One selected  $x_1, x_2... x_{100}$  - roots of  $f_1, f_2, ... f_{100}$  respectively.What is the value of sum  $f_2(x_1)+...+f_{100}(x_{99})+f_1(x_{100})?$ ---------
Also 9.1 in 3rd round of Russian National Olympiad

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