= Solution
If $F\dashv U$, let $1$ denote a singleton <set>. The <adjunction> gives the natural <bijections>
$$
U(C)\cong\mathbf{Set}(1,U(C))\cong\mathcal C(F1,C).
$$
Thus \b[$U$ is represented by $F1$], proving $A\Rightarrow R$.
If $U\cong\mathcal C(R,-)$ is a covariant <representable functor>, a <morphism> $R\to\lim_jC_j$ is exactly a compatible family of <morphisms> $R\to C_j$. Consequently the comparison map
$$
\mathcal C(R,\lim_jC_j)\longrightarrow\lim_j\mathcal C(R,C_j)
$$
is a <bijection> for every existing small <categorical limit>. This proves $R\Rightarrow L$ by the <universal property> of a limit. In particular,
$$
\boxed{A\Rightarrow R\Rightarrow L.}
$$
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