
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
For certain real numbers \( p \), \( q \), and \( r \), the polynomial
\[ h(x) = x^3 + px^2 + 2x + 20 \]
has three distinct roots, and each root of \( h(x) \) is also a root of the polynomial
\[ j(x) = x^4 + 2x^3 + qx^2 + 150x + r. \]
What is \( j(1) \)?

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