
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
For the equation in terms of $x$: $8x^{2} - mx + (m - 6) = 0$, what is the range of values for $m$ such that the roots of the equation are:
(1) Both positive;
(2) Both negative;
(3) Of opposite signs?

Present the answer in LaTex format: \boxed{Your answer}
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