Variadic template with function, inputs and outputs types

I'm trying to understand how to create and call variadic templates with function, inpus args and output args types. I wrote this toy example:

#include <tuple>

template<typename Func, typename... Inputs, typename... Outputs>
std::tuple<double, Outputs...> foo(int init, Func&& func, Inputs&&... args) {
    return std::forward<Func>(func)(init, std::forward<Inputs>(args)...);
};

int main () {
    int init = 6;
    double mult = 2.3;
    std::tuple<double, double> bar = foo(
        init,
        [](int init_, double mult_) { 
            double res = init_ * mult_;
            return std::make_tuple(res, 4.1);
        },
        mult
    );
    int out = std::get<0>(bar);
    return out;
}

However, it doesn't compile. How should I modify it to get 13 as result?

I get this error message:

<source>: In function 'int main()':
<source>:11:41: error: conversion from 'tuple<double>' to non-scalar type 'tuple<double, double>' requested
   11 |     std::tuple<double, double> bar = foo(
      |                                      ~~~^
   12 |         init,
      |         ~~~~~                            
   13 |         [](int init_, double mult_) {
      |         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~    
   14 |             double res = init_ * mult_;
      |             ~~~~~~~~~~~~~~~~~~~~~~~~~~~  
   15 |             return std::make_tuple(res, 4.1);
      |             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   16 |         },
      |         ~~                               
   17 |         mult
      |         ~~~~                             
   18 |     );
      |     ~                                    
<source>: In instantiation of 'std::tuple<double, Outputs ...> foo(int, Func&&, Inputs&& ...) [with Func = main()::<lambda(int, double)>; Inputs = {double&}; Outputs = {}]':
<source>:18:5:   required from here
<source>:5:72: error: could not convert 'main()::<lambda(int, double)>(init, std::forward<double&>((* & args#0)))' from 'tuple<double, double>' to 'tuple<double>'
    5 |     return std::forward<Func>(func)(init, std::forward<Inputs>(args)...);
      |                                                                        ^
      |                                                                        |
      |                                                                        tuple<double, double>