  Coherence and entanglement are fundamental concepts in resource theory. The
coherence (entanglement) of assistance is the coherence (entanglement) that can
be extracted assisted by another party with local measurement and classical
communication. We introduce and study the general coherence of assistance.
First, in terms of real symmetric concave functions on the probability simplex,
the coherence of assistance and the entanglement of assistance are shown to be
in one-to-one correspondence. We then introduce two classes of quantum states:
the assisted maximally coherent states and the assisted maximally entangled
states. They can be transformed into maximally coherent or entangled pure
states with the help of another party using local measurement and classical
communication. We give necessary conditions for states to be assisted maximally
coherent or assisted maximally entangled. Based on these, a unified framework
between coherence and entanglement including coherence (entanglement) measures,
coherence (entanglement) of assistance, coherence (entanglement) resources is
proposed. Then we show that the coherence of assistance as well as entanglement
of assistance are strictly larger than the coherence of convex roof and
entanglement of convex roof for all full rank density matrices. So all full
rank quantum states are distillable in the assisted coherence distillation.
