
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
A student, waking up at the end of an algebra class, heard only part of the teacher's phrase: "... I will just say that all roots are real and positive." Looking at the board, he saw a 20th-degree equation assigned for homework and tried to quickly write it down. He managed to write only the first two terms \( x^{20} - 20x^{19} \) before the teacher erased the board; however, he remembered that the constant term was +1. Can you help our unfortunate hero solve this equation?

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