
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  $x$ - minimal root of equation  $x^2-4x+2=0$ . 
Find two first digits of number  $ \{x+x^2+....+x^{20} \}$  after  $0$ , where  $\{a\}$ - fractional part of  $a$ .

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