
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 \(\alpha\) and \(\beta\) be the roots of \(x^{2}-4x+c=0\), where \(c\) is a real number. If \(-\alpha\) is a root of \(x^{2}+4x-c=0\), find the value of \(\alpha\beta\).

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