
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 positive integers \( x, y, z \) satisfying \( xyz = (22-x)(22-y)(22-z) \) and \( x + y + z < 44 \). Let \( M \) and \( N \) represent the maximum and minimum values of \( x^2 + y^2 + z^2 \) respectively. Find \( M + N \).

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