
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 that the graph of a quadratic function has two intersection points $A$ and $B$ with the $x$-axis, which are symmetric about the line $x=-1$, and $AB=6$. The vertex of the function lies on the graph of $y=2x$. Find the expression of this quadratic function.

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