
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
Let $f(x) = (m+1)x^2 - mx + m - 1$.

(1) When $m=1$, find the solution set of the inequality $f(x) > 0$;  
(2) If the solution set of the inequality $f(x) + 1 > 0$ is $\left( \frac{3}{2}, 3 \right)$, find the value of $m$.

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