
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 \[ h(x) = x^3 + px^2 + 2x + 15 \] has three distinct roots, and each root of $h(x)$ is also a root of the polynomial \[ k(x) = x^4 + x^3 + qx^2 + 150x + r. \] What is $k(1)$?

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