
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 quadratic polynomial with real coefficients, $p(x)$, is termed as *mysterious* if $p(p(x))=0$ has exactly four real roots, including multiplicities. Find the polynomial $p(x)$ such that its leading coefficient is $1$, the sum of its roots is minimal, and calculate $p(0)$.
**A)** $2$
**B)** $3$
**C)** $4$
**D)** $5$

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