Test bench: verilog task control

I have a strange question with regards to task control in verilog test bench, so please bear with my attempt to trying to keep it to a simple form.

I have a task flow inside a file, for which I am not permitted to change anything. For example;

1) File: Faults

task examine; begin task a(); task b(); end

the explanations for task a and b are also inside the file-Fault for which I am not permitted to make any changes.

However I am using the above task in my test case 2) File : Testcase_1

task xyz; task examine; task hml; etc..

however there is a problem with task a. when task-a runs, there is a variable inside that task which is changing wrongly and I have to force the variable to follow the right formula somewhere else and correct it without doing the task correction in the Faults file.

I have access to another file called as File: utility where I can write the correct formula to force the variable to follow the new formula, get changed and then continue executing with task b and so on in my test case and produce the results.

But I dont know how can I stop task a in the middle and then change the variable(force it follow a new formula and get the right value) and then continue with task b and so on. Can anybody help me with this???

I am happy to provide additional info if required. Thanks in advance