
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 $y=3x^2-6x+5$, if its vertex remains unchanged, the direction of its opening is reversed, and then it is translated along the axis of symmetry, a new parabola is obtained. This new parabola intersects with the line $y=mx-2$ at the point $(2, 4)$. Find the equation of the new parabola.

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