
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
Find the vertex and the y-intercept of the parabola represented by the equation $y = 3x^2 - 6x + 2$.
A) Vertex: $(1, -1)$, y-intercept: $(0, 1)$
B) Vertex: $(0, 2)$, y-intercept: $(1, -1)$
C) Vertex: $(1, -1)$, y-intercept: $(0, 2)$
D) Vertex: $(2, 3)$, y-intercept: $(1, -1)$

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