How to gracefully get out of AbandonedMutexException?

I use the following code to synchronize mutually exclusive access to a shared resource between several running processes.

The mutex is created as such:

Mutex mtx = new Mutex(false, "MyNamedMutexName");

Then I use this method to enter mutually exclusive section:

public bool enterMutuallyExclusiveSection()
{
    //RETURN: 'true' if entered OK, 
    //         can continue with mutually exclusive section
    bool bRes;

    try
    {
        bRes = mtx.WaitOne();
    }
    catch (AbandonedMutexException)
    {
        //Abandoned mutex, how to handle it?

        //bRes = ?
    }
    catch
    {
        //Some other error
        bRes = false;
    }

    return bRes;
}

and this code to leave it:

public bool leaveMutuallyExclusiveSection()
{
    //RETURN: = 'true' if no error
    bool bRes = true;

    try
    {
        mtx.ReleaseMutex();
    }
    catch
    {
        //Failed
        bRes = false;
    }

    return bRes;
}

But what happens is that if one of the running processes crashes, or if it is terminated from a Task Manager, the mutex may return AbandonedMutexException exception. So my question is, what is the graceful way to get out of it?

This seems to work fine:

catch (AbandonedMutexException)
    {
        //Abandoned mutex
        mtx.ReleaseMutex();
        bRes = mtx.WaitOne();    
    }

But can I enter the mutually exclusive section in that case?

Can someone clarify?