Each successive StEP is both the object and result of the one that precedes it.
Working "forward" in order, Noticing what is is the objective of Observing what is. Recognition of what is is the objective of Noticing what is. Acknowledgement of what is is the objective of Recognizing what is. Acceptance of what is is the objective of Acknowledging what is. Ownership of what is is the objective of Accepting what is. And Appreciation of what is is the objective of Owning what is.
Working "backward," Appreciating what is is the result of Owning what is. Owning what is is the result of Accepting what is. Accepting what is is the result of Acknowledging what is. Acknowledging what is is the result of Recognizing what is. Recognizing what is is the result of Noticing what is. And Noticing what is is the result of Observing to see, hear, feel and sense what is.
Those first seven ACTions (see the links to Steven Hayes's views of what psychotherapeutic ACTion is -- and is not -- below) seem to kick-start an at-first linear, but then cyclical, feedback-looping process that begins at the eighth "StEP," which is Understanding in precisely the manner described by Jiddu Krishnamurti in lecture after lecture and book after book (see below). (In Krishnamurti's view, "understanding" was only possible as the result of unfettered, uncontaminated, empirical observation. Period.)
Understanding is more of an arrival or automatic result of the ACTions taken in the previous seven StEPs. But one has to get there to kick the door open to the Detachment (as in Buddhist parlance), De-Fusion (as per Hayes et al), Digestion or metabolization of the neurochemistry driving the affective states (e.g.: worry, remorse, regret, anxiety, grief, frustration, anger, rage) and Discharge that will also occur "automatically" at the ninth StEP if one continues to stay in the process by just Observing, Noticing, Recognizing, etc.
BUT (and this is a very major but)... one has to know experientially what all of the labels of each StEP mean. And the only way I know of to get that down is to apply mindfulness skills when one reads the definitions of each of those terms, pretty much -- though not necessarily exactly -- as I ran them down from online dictionary definitions in the post at http://pairadocks.blogspot.com/2015/04/the-10-steps-of-emotion-processing.html.
Thereafter, it just comes down to using the StEPs in fairly much -- though not necessarily precisely -- the order I suggested. Because I do see that use in actual context may not work in that exact order, or even that all of the StEPs are required. (I often drop StEP six -- or Own -- out, because it doesn't fit in the context of some circumstance I am looking into "mindfully.")
Hayes links: https://contextualscience.org/ and
Krishnamurti links: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=jiddu%20krishnamurti%20books
Object Relations links: https://en.wikipedia.org/wiki/Object_relations_theory,
(Don't get too hung up about grasping O/R if you're not a professional; the stuff requires a lot of "pre-requisites" to get one's mind wrapped around it for most people.)
A later addition:
I had not read -- or even heard of -- Stephen Batchelor's Buddhism Without Beliefs: A Contemporary Guide to Awakening (New York: Riverhead / Penguin, 1997). I found it recently when I began to dig into an increasing conflict between Buddhist meditation as a psychotherapeutic "practice" or "method" and Buddhism, a collection of proscribed doctrines, dogmas and beliefs.
Batchelor did me the considerable favor of both fleshing out and clarifying my own concerns about the "institutional religification" of what Siddartha Gautama came up with 2500 years ago as an existential psychotherapy for the resolution of anguish. Anguish, according the Buddha, was functionally relieved by observation, perception, recognition, acceptance, ownership, appreciation and understanding of its existence, its origins in craving and attachment, its cessation and the path thereto.
Thus, all I have really done in the development of the 10 StEPs is re-dis-cover the Same Old Truth, albeit with the considerable help of those cited in the list of resources following the later article at http://pairadocks.blogspot.com/2016/04/the-10-steps-for-recovery-from.html and highlighted immediately below:
Stephen Batchelor, Stanley & Carolyn Block, Tara Brach, Pema Chodron, Arthur Deikman, Daniel Goleman, William Hart & S. N. Goenka, Stephen Hayes et al, Jean Klein, Joel Kramer & Diana Alstad, Jon Kabat-Zinn, Jiddu Krishnamurti, Stephen Levine, Marsha Linehan, Daniel Siegel, Charles Tart, Eckhart Tolle, Chogyam Trungpa, Sheri van Dijk, Alan Watts, and Mark Williams et al.
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