
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
The expression \(x^2 + 19x + 88\) can be written as \((x + a)(x + b)\), and the expression \(x^2 - 23x + 132\) can be written as \((x - b)(x - c)\), where \(a\), \(b\), and \(c\) are integers. What is the value of \(a + b + c\)?

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