
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 $a \in \mathbb{R}$, and consider the quadratic function $f(x) = ax^2 - 2x - 2a$. If the solution set of $f(x) > 0$ is $A$, and $B=\{x \mid 1 < x < 3\}$, with $A \cap B \neq \emptyset$, find the range of values for the real number $a$.

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