
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
Given the function \( y = f(x) \) where \( x \in D \), if there exists a real number \( c \in D \) such that \( f(c) = 0 \), then \( x = c \) is called a zero of the function \( y = f(x) \). In fact, the zero of the function is the x-coordinate of the point where the function's graph intersects the x-axis.

(2007 - Guangdong) Given that \( a \) is a real number and the function \( f(x) = 2ax^2 + 2x - 3 - a \), if the function \( y = f(x) \) has a zero in the interval \([-1, 1]\), find the range of values for \( a \).

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