How to compute the median month in R

I have a dataframe df with several locations var1 and var2. For every year for these locations the months where the temperature reaches an annual maximum maxmo or minimum minmo is given. I want to calculate the median month over the available years for which a certain location reaches an annual maximum or minimum.

df <- data.frame(
        variable = c("var1","var1","var1","var1","var2", "var2","var2","var2"), 
        year = c(2007:2010,2012:2015), 
        maxmo = c(10,8,8,7,7,8,8,8), 
        minmo=c(12,12,1,1,1,1,2,2))

I tried this

df %>%
  group_by(variable)%>%
  summarize(maxmo2= median(maxmo), minmo2=median(minmo))

which gives me

  variable maxmo2 minmo2
  <chr>     <dbl>  <dbl>
1 var1          8    6.5
2 var2          8    1.5

while I want to get

  variable maxmo2 minmo2
  <chr>     <dbl>  <dbl>
1 var1          8    12.5
2 var2          8    1.5

or

  variable maxmo2 minmo2
  <chr>     <dbl>  <dbl>
1 var1          8    0.5
2 var2          8    1.5

So var1 situates between December and January (12.5 or 0.5)

Map the months to a 24 clock and use the circular package:

library(circular)
library(dplyr)

med <- function(x, eps = 0.01) {
  cir <- circular(2 * (x - 1), units = "hours")
  num <- as.numeric(median(cir)) %% 24
  ((num + (num > (24 - eps))) %% 24) / 2 + 1
}
 
df %>%
  group_by(variable) %>%
  summarize(across(starts_with("m"), med), .groups = "drop")

giving

# A tibble: 2 x 3
  variable maxmo minmo
  <chr>    <dbl> <dbl>
1 var1         8  12.5
2 var2         8   1.5