Adverse Possession: Is It Worth Getting a Property Boundary Survey when Opposing Party is a Municipality

My question involves real estate located in the State of: California

The City of Los Angeles is claiming now (after not saying anything to the contrary for decades) that my retail shopping center located on a busy street corner has been encroaching onto public property and wants to shave off the outer 15% or so of the edges to the existing property boundary lines in order to widen the adjacent sidewalks.

I understand that adverse possession against a municipality will basically not work....and so what remedies (if any) do I have?

But more importantly....my questions are:

1. Will getting a professional survey done (for a cost of $2,500-$4,500) do anything to affect the City's determination that my property has been encroaching on public property?

2. If I do expend the money for a professional survey and that survey establishes that the City's boundary claims are incorrect...wouldn't the City basically argue the contra and claim that its survey trumps over mine in order to get what they want anyway?

3. In the event the City trumps over any of my claims to the contrary (re: its views regarding the borderlines) would the City (at the least) "compensate" for this "de-facto taking" since after all I did pay taxes on that "disputed portion" all these years?

Thanks in advance for any possible opinions on this sticky matter.....

Adverse Possession: Is It Worth Getting a Property Boundary Survey when Opposing Party is a Municipality