
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, axis of symmetry, and $y$-intercept of the parabola given by the equation $y = 3x^2 + 6x + 5$.
A) Vertex: $(-1, 1)$, Axis of Symmetry: $x = -1$, $y$-intercept: $y = 3$
B) Vertex: $(1, 2)$, Axis of Symmetry: $x = 1$, $y$-intercept: $y = 5$
C) Vertex: $(-1, 2)$, Axis of Symmetry: $x = -1$, $y$-intercept: $y = 5$
D) Vertex: $(1, -2)$, Axis of Symmetry: $x = 1$, $y$-intercept: $y = 3$

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