Getting Type + ConstructorInfo from ObjectCreationExpressionSyntax

I'm trying to get type and constructor info out of an ObjectCreationExpressionSyntax element.

I first need to assess that the created instance is an ArgumentException or a class that derives from it. Then, I need to get the ConstructorInfo (System.Reflection) that's being used.

public override void Initialize(AnalysisContext context)
{
    context.RegisterSyntaxNodeAction(c =>
    {
        var local = c.Node as ObjectCreationExpressionSyntax;

        if (local == null)
            return;

        ArgumentSyntax paramNameArgument;
        bool conditionsAreMet;

        // the code that's required to get both the Type and ConstructorInfo instances would go here

        if (conditionsAreMet)
        {
            c.ReportDiagnostic(Diagnostic.Create(Rule, paramNameArgument.GetLocation()));
        }
    }, SyntaxKind.ObjectCreationExpression);
}

The ObjectCreationExpressionSyntax has a Type property, which I'm pretty sure will be the starting point. However, I don't quite understand how am I supposed to extract anything from it.

Any guidance would be much appreciated.