Trouble with nested ifelse statement in R

I'm trying to run a nested ifelse statement in R. Here's a look at the structure of my data using the glimpse() function from the tidyverse:

Rows: 22,104
Columns: 9
$ `Formation/Locality`    <chr> "Montmartre", "Montmartre", "Montmartre", "Fur", "Me...
$ Location                <chr> "Ile-de-France Region, France", "Ile-de-France Regio...
$ Environment             <chr> "terrestrial", "terrestrial", "terrestrial", "offsho...
$ `Palaeolongitude(N/-S)` <dbl> 47.4, 47.4, 47.4, 52.3, 46.9, 42.9, 47.5, 46.9, 46.2...
$ `Palaeolatitude(E/-W)`  <dbl> 1.6, 1.6, 1.6, 5.4, 4.8, 1.9, -5.2, 4.8, -93.6, -111...
$ TaxonomicLevel          <chr> "Order", "Order", "Order", "Order", "Order", "Order"...
$ TaxonomicName           <chr> "Upupiformes", "Upupiformes", "Upupiformes", "Trogon...
$ MinMax                  <chr> "MaxMa", "MaxMa", "MaxMa", "MaxMa", "MaxMa", "MaxMa"...
$ Age                     <dbl> 37.2, 37.2, 37.2, 55.8, 48.6, 37.2, 48.6, 48.6, 55.8...

I'm trying to get R to look at the Age column and if the value is within a certain range, for it to put the geological age name into a new column called AgeName. If the value is not within the range, I want it to move on to the next age range and so on and so forth. Here's my code so far:

pbdb_tidyish$AgeName <- ifelse(56>=pbdb_tidyish$Age&&47.8<pbdb_tidyish$Age,
                               "Ypresian",
                               ifelse(47.8>=pbdb_tidyish$Age&&41.2<pbdb_tidyish$Age,
                                      "Lutetian",
                                      ifelse(41.2>=pbdb_tidyish$Age&&37.8<pbdb_tidyish$Age,
                                             "Bartonian",
                                             ifelse(37.8>=pbdb_tidyish$Age&&33.9<=pbdb_tidyish$Age,
                                                    "Priabonian",NA))))

When I run this code, it creates the new column but fills the whole column with "Priabonian" so the dataset now looks like this:

Rows: 22,104
Columns: 10
$ `Formation/Locality`    <chr> "Montmartre", "Montmartre", "Montmartre", "Fur", "Me...
$ Location                <chr> "Ile-de-France Region, France", "Ile-de-France Regio...
$ Environment             <chr> "terrestrial", "terrestrial", "terrestrial", "offsho...
$ `Palaeolongitude(N/-S)` <dbl> 47.4, 47.4, 47.4, 52.3, 46.9, 42.9, 47.5, 46.9, 46.2...
$ `Palaeolatitude(E/-W)`  <dbl> 1.6, 1.6, 1.6, 5.4, 4.8, 1.9, -5.2, 4.8, -93.6, -111...
$ TaxonomicLevel          <chr> "Order", "Order", "Order", "Order", "Order", "Order"...
$ TaxonomicName           <chr> "Upupiformes", "Upupiformes", "Upupiformes", "Trogon...
$ MinMax                  <chr> "MaxMa", "MaxMa", "MaxMa", "MaxMa", "MaxMa", "MaxMa"...
$ Age                     <dbl> 37.2, 37.2, 37.2, 55.8, 48.6, 37.2, 48.6, 48.6, 55.8...
$ AgeName                 <chr> "Priabonian", "Priabonian", "Priabonian", "Priabonia...

Does anyone have any idea where I'm going wrong? I think it's just looking at the first Age value, running the ifelse statement then filling the whole column with the result of that as opposed to moving on to the next row.

Thanks,

Carolina