
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
Let \(a\), \(b\), and \(c\) be real numbers. If 1 is a root of \(x^{2} + ax + 2 = 0\) and \(a\) and \(b\) are roots of \(x^{2} + 5x + c = 0\), find the value of \(a + b + c\).

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