Design a two$-$tape TM for

L $=\{$a$^$nb$^2$nc$^$n$\},$n $1,=\{$a$,$ b$,$ c$\}.$

You must use the second tape and leave the input in its original condition; however, you may do what you want with the second tape. You may use the stay option, in addition to left and right.

Provide:

$1.$ the algorithm used

$2.$ a JFLAP TM image including$$each states' meaning using the "Change Label" option in JFLAP

$3.$ Show image of at least $10$ test cases $($good and bad$)$ to fully prove that TM is functional.

$4.$ a detailed description of whether the TM works or not, if not, to what extent.