Count the longest stretch of consecutive patterns

I have a sequence file:

$ cat file
CACCGTTGCCAAACAATG
TTAGAAGCCTGTCAGCCT
CATTGCTCTCAGACCCAC
GATGTACGTCACATTAGA
ACACGGAATCTGCTTTTT
CAGAATTCCCAAAGATGG

I want to calculate the longest stretch of C+T. I could only count total C+T, but I want the longest stretch.

$ cat file | awk '{ print $0, gsub(/[cCtT]/,"",$1)}'
CACCGTTGCCAAACAATG 9
TTAGAAGCCTGTCAGCCT 10
CATTGCTCTCAGACCCAC 12
GATGTACGTCACATTAGA 8
ACACGGAATCTGCTTTTT 11
CAGAATTCCCAAAGATGG 7

The *Expected result* would be to show the longest C+T stretch.

CACCGTTGCCAAACAATG 9 2
TTAGAAGCCTGTCAGCCT 10 3
CATTGCTCTCAGACCCAC 12 5
GATGTACGTCACATTAGA 8 2
ACACGGAATCTGCTTTTT 11 6
CAGAATTCCCAAAGATGG 7 5