
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
Consider the equation \(y = ax^2 + bx + c\) for which the graph is a parabola with a vertex at \((4, 3)\) and a vertical axis of symmetry. The parabola also passes through the point \((2, 5)\). Determine the values of \(a\), \(b\), and \(c\).

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