
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 the quadratic function \( y = ax^2 + bx + c \). The graph of this function lies above the line \( y = -2x \) if and only if \( 1 < x < 3 \).

(1) If the equation \( ax^2 + bx + 6a + c = 0 \) has two equal real roots, find the expression of the quadratic function.

(2) If the quadratic function has a maximum value that is positive, find the range of values for \( a \).

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