
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
Given the solution set of the inequality regarding $x$, $x^2 - ax - 2 > 0$, is $\{x | x < -1 \text{ or } x > b\}$ where $b > -1$,
(1) Find the values of $a$ and $b$;
(2) When $m > -\frac{1}{2}$, solve the inequality $(mx + a)(x - b) > 0$ for $x$.

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