
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
If \( x^{2} + ax + 48 = (x + y)(x + z) \) and \( x^{2} - 8x + c = (x + m)(x + n) \), where \( y, z, m \), and \( n \) are integers between -50 and 50, find the maximum value of \( ac \).

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