
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
We say that the constant \(a\) is a fixed point of a function \(f\) if \(f(a) = a\). Find all values of \(c\) such that \(f(x) = x^2 - 2\) and \(g(x) = 2x^2 - c\) share a common fixed point.

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