can't make my ForwardDiff.gradient function work

Question

I want to find the gradient of a function "lifetime_reward" by using ForwardDiff.gradient. "lifetime_reward" calls 4 other functions called "U", "U_prime", "steady_state" and "ramsey_simul".

lifetime_reward

   function lifetime_reward(model, a::Vector, s::AbstractVector)::Number
       Β = [model.β^i for i in range(1, 50, length=50)]
    
       C = ramsey_simul(model, a, s)[4][2:51]

       V = sum(Β.*C)

       return V

   end

U and U_prime

   U(x, model) = (x^(1-model.γ))/(1-model.γ)
   U_prime(x, model) = x^(-model.γ)    

steady_state

   function steady_state(model, a)
       k_A = 1 - model.β*U_prime(1, model)*(1-model.δ)
       k_B = model.β*U_prime(1, model)*model.α*exp(a)

       k = k_A/k_B
       k = k^(1/(model.α - 1))

       y = exp(a)*(k^model.α)
   
       i = k - (1-model.δ)k

       c = y - i

       return k, y, i, c

   end

ramsey_simul

   function ramsey_simul(model, a::Vector, s::AbstractVector)  
       T = length(a)
       a0 = 0
       ss = steady_state(model, a0)

    

       k = ss[1]
       y = ss[2]
       i = ss[3]
       c = ss[4]


       V1 = [k]
       V2 = [y]
       V3 = [i]
       V4 = [c]

    
       for t=1:T
           k = (1-model.δ)*k + i 
        
           y = exp(a[t])*(k^model.α) 

           i = y*s[t] 

           c = y - i

           push!(V1, k)
           push!(V2, y)
           push!(V3, i)
           push!(V4, c)
    
       end

    
       return V1, V2, V3, V4

   end

I redefine lifetime_reward as function of s only :

   lr(s) = lifetime_reward(model, a, s)

And then I try runnig this command :

   ForwardDiff.gradient(lr, s_plot)

With :

   s_plot = range(0.2, 0.3, length=50)

but this sends me :

   MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(lr),   Float64}, Float64, 10})
   Closest candidates are:
     (::Type{T})(::Real, !Matched::RoundingMode) where T<:AbstractFloat at rounding.jl:200
     (::Type{T})(::T) where T<:Number at boot.jl:772
     (::Type{T})(!Matched::AbstractChar) where T<:Union{AbstractChar, Number} at char.jl:50
     ...

   Stacktrace:
    [1] convert(#unused#::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(lr),   Float64}, Float64, 10})
      @ Base ./number.jl:7
    [2] push!(a::Vector{Float64}, item::ForwardDiff.Dual{ForwardDiff.Tag{typeof(lr), Float64}, Float64, 10})
      @ Base ./array.jl:1057

Can someone help me ? I am new to this package and not sure how its is working under the hood.

I guess this is a problem of type used and I bet my V1, V2, V3, V4 are not efficient in ramsey_simul. I already tried to change their types but what I did, dit not change the error.