With you doing nothing at all? The people this was written to had already done something.
Philippians 2:12 Wherefore, my beloved, as ye have always obeyed, not as in my presence only, but now much more in my absence, work out your own salvation with fear and trembling.
In the next verse we read:
13 For it is God which worketh in you both to will and to do of his good pleasure.
Why did they already do something as you said ("always obeyed")? Work is immediately attributed to God, God worked in them first to desire righteousness, and then do things He liked. They are defined as a receiving participant.
Mary the mother of Jesus, as an example. Did she knit her body to be healthy and fertile, or initiate puberty? Did she engage in anything to bring pregnancy about, or even ask God for one? Did she deliver herself from stoning by an angry mob? Did she deliver Jesus from Herod? Did she guarantee by her will and effort not to miscarry or have stillbirth? Did she facilitate the travail or break water?
None of this is her work. Yet Mary is a participant in God's plan. But she must be doing something? She did receive (heard and believed) the Word of God to start with. She is a vessel for God's use. "Let everything you have said happen to me". God does not share His glory, but we are involved. I'd say our participation is one of receiving.
We can't boast, because we are receiving something that could not originate from us. Being a receiving participant isn't something we can claim as work, but I don't think receiving is
doing nothing, either, if we look at receiving in Biblical context. Receiving isn't exactly a work, but also isn't exactly doing nothing, it's being still. Being still and accepting what God gives is a lot harder to do than jumping in with our ideas, which is a movement from the flesh, and comes very easy and naturally to man. By receiving, as opposed to us trying to act on our own, we mortify the works of the flesh.