
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 propositions p and q, where p is the statement that the inequality $x^2 + (a-1)x + 1 \leq 0$ has an empty solution set, and q is the statement that the equation $\frac{x^2}{2} + \frac{y^2}{a} = 1$ represents an ellipse with foci on the y-axis. If the negation of q is true and the disjunction p ∨ q is true,
1. Determine the range of the real number a;
2. Determine the shape of the curve represented by the equation $(a+1)x^2 + (1-a)y^2 = (a+1)(1-a)$.

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