$\backslash$table$[[$Current State,Signal from Outside,top$($Stack$),$Successor State,Operation$],[$start$,[,$nothing $//$ is empty,up$,$push$([)],[$up$,[,[,$up$,$push$([)],[$up$,],[,$down,pop$],[$down$,],[,$down,pop$],[$down$,$none $//$ have ended,nothing $//$ is empty,accept,none $//$ do nothing$]]$

In this mysterious machine's user manual the friends have read that this machine, which must be set into the "start" state at the beginning, consumes exactly one signal symbol from the outside for each of its operations. In other words:

it is not possible for this machine to do more operations than it received signals from the outside, and

it is also not possible for this machine to do fewer operations than it received signals from the outside.

Moreover, the friends are also reading in the user manual that this machine's initial stack is always empty at the start.

Last but not least the user manual also warns that this machine can possibly get stuck upon receiving a signal which does not "fit" into the machine's pre$-$defined work plan.

a$)[0\mathrm{.}6$ Points$]$: Front page of your work sheet.

Donald Doesntknow now sets the machine into its start state and sends the following sequence of signals one by one, from left to right $-$ to the machine:

$[[[]]]$

YOUR TASK

Explain to Donald Doesntknow in detailed steps what the machine is doing while it is receiving Donald's six signals.