
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 the monic quadratic polynomials P(x) and Q(x), with P(Q(x)) having zeros at x=-23, -21, -17, and -15, and Q(P(x)) having zeros at x=-59,-57,-51, and -49, determine the sum of the minimum values of P(x) and Q(x).

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