1: Piaget's own definitions
Origins of Intelligence [1936/1953]
p32: accommodation cannot be dissociated from assimilation

Play, Dreams and Imitation [1945/1951]
p5: Imitation is a continuation of the effort at accommodation
p278: Piaget's account of Frege's sense/reference [aka signifier/signified] requires both assimilation and accommodation in one act
[in Judgment and Reasoning 1924/1928,p.173 Piaget had contrasted assimilation with imitation, now here qualified/corrected]
This text also gives examples of their differing proportions

Equilibration if Cognitive Structures [1975/1985]
p.6: every assimilatory scheme has to be accommodated to the elements it assimilates

2: Piaget's Rationale
The main reason why is given in Piaget's first book Recherche (1918). In physical systems, two forces acting on an object generate a specific movement [say, 2 air jets on a ball on a billiard table making the ball move to the top right corner, i.e one outcome]. The final movement is their outcome, and the causes behind it can be left out in following this outcome movement. But in mental systems, more is required since this condition has also to be met:

In the 1918 text, the general claim is made that if 2 premises entail a valid conclusion, an adequate understanding of this requires the person to understand this conclusion as a conclusion from these premises. That is, the conclusion is understood as an inference only through its entailing premises. For example

(1) The wine is red Cabernet Sauvignon or white Sauvignon Blanc
(2) The wine is not red
therefore
(3) The wine is Sauvignon Blanc

Though (3) can be understood in and of itself, it can be understood as an entailment only in terms of (1) and (2) and their deductive relation to (3).
Reversible reasoning is this bi-directional linkage between these elements [1-3] in this whole [the valid deduction of 3 by 1 + 2]. Reasoning is irreversible when this condition is not met.

As Piaget put this: [With regard to irreversible reasoning] a subject cannot keep a premise identical with itself throughout a¡¡mental experiment [J&R, 1924/1928. p.239]

In short,¡¡a person has to retain the premises and conclusion as separate elements with their own identity [accommodation] and also to make the advance which is to grasp the deductive conclusion of 3 by 1 + 2 [assimilation].

The claim that these constructs are functional is explicit in Piaget's paper in Mind (1931). He used different logical models throughout his 60 years work to interpret the framework used capture the [assimilating] whole, where its parts or elements are inputs from accommodatory aspects of the human mind in action.