
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 quadratic function $f(x)=ax^{2}+bx+c$, the solution set of the inequality $f(x) > -2x$ is $\{x|1 < x < 3\}$.
- (I) If the equation $f(x)=2a$ has two equal positive roots, find the expression of $f(x)$;
- (II) If the maximum value of $f(x)$ is positive, find the range of $a$.

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