
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 a quadratic function $y=ax^2+bx+c$, and the solution to the inequality $ax^2+bx+c>-2x$ is $1<x<3$  
(1) If the equation $ax^2+bx+c+6a=0$ has two equal roots, find the expression of the quadratic function;  
(2) If the maximum value of $y=ax^2+bx+c$ is positive, find the range of values for $a$.

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