
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
A fixed point of a function \( f \) is a value of \( x \) for which \( f(x) = x \). Let \( f \) be the quadratic function defined by \( f(x) = x^2 - c x + c \) where \( c \in \mathbb{R} \). Find, in interval notation, the set consisting of all values of \( c \) for which \( f \circ f \) has four distinct fixed points.

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