Multiple if else statements to classify existing values in a new column in R

I have tried reproducing the method described in this post (Trying to create a new column using multiple if else statements in R)

I would like to classify the severity of a patients blood work. My intention is to give a certain score (i.e. 0, 1, 2, 3) to an already existing value for each patient's blood work value. After that, I want to save these new values into a new column. The cut off values are:

if value is >=150000, score = 0
if value is <150000, score = 1
if value is <100000, score = 2
if value is <50000, score = 3
if value is <20000, score = 4

dput is

> dput (platelets_v1)
structure(list(ID = c(13055908, 13059026, 13154920, 13201107, 
13207119, 13207948, 13234892, 13261022, 13082943, 13193903, 13259391, 
13283776, 13262499, 13154288, 13207315, 13269178, 13135316, 13055690, 
13207670, 13220627, 13233898, 13055009, 13044947, 13181075, 13261607, 
13186960, 13240091, 13060589, 13201616, 13260671, 13302375, 13021555, 
13054278, 13062360, 13035346, 13077712, 13128769, 13267480, 13160156, 
13040172, 13160971, 13239318, 12977871, 13090190, 13321288, 13040530, 
13100979, 13124511, 13192142, 13289317, 13315577, 13154966, 13044653, 
13079694, 13128639, 13165362, 13207352, 13049409, 12999835, 13210994, 
13283675, 13223721, 13064865, 13104602, 13036280, 13040507, 12964437, 
13029805, 13029001, 12993036, 13072516, 13060586, 13119819, 13040632
), platelets = c("469.000", "NA", "NA", "243.000", "NA", "NA", 
"NA", "334.000", "522.000", "NA", "NA", "NA", "NA", "312.000", 
"421.000", "NA", "321.000", "NA", "NA", "NA", "298.000", "263.000", 
"109.000", "280.000", "NA", "NA", "430.000", "288.000", "159.000", 
"528.000", "NA", "163.000", "NA", "439.000", "NA", "477.000", 
"NA", "473.000", "NA", "459.000", "183.000", "343.000", "285.000", 
"459.000", "253.000", "NA", "227.000", "NA", "569.000", "NA", 
"NA", "NA", "239.000", "382.000", "270.000", "NA", "362.000", 
"NA", "146.000", "367.000", "NA", "531.000", "NA", "363000", 
"NA", "257000", "158000", "56000", "417", "NA", "171000", "NA", 
"NA", "NA")), row.names = c(NA, -74L), class = c("tbl_df", "tbl", 
"data.frame"))

I have tried the following:

> labels <- c('0', '1', '2','3', '4')
> breaks <- c(500000, 150000, 100000, 50000, 20000)
> teste01 <- platelets_v1 %>% mutate(platelets_v1 = cut(platelets_v1, breaks = breaks, labels = labels, include.lowest = TRUE))

Desired result:

ID platelets score
13055908 469000 0
13059026 NA NA
13154920 NA NA
13201107 243000 0

and so on

Any light would be greatly appreciated.