
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
How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of coefficients, with the additional condition that one of the coefficients must always be $1$?
**A)** 0
**B)** 1
**C)** 2
**D)** 3
**E)** Infinitely many

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