
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
Given two numbers whose sum is 15 and product is 36, find the roots of the polynomial and provide the equation of the polynomial after all the roots are increased by 3.
A) $x^2 - 15x + 36$
B) $x^2 - 11x + 30$
C) $x^2 - 21x + 90$
D) $x^2 - 18x + 72$

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