
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 propositions $p: \exists x\_0 \in [-1,1]$ such that $x\_0^2 + x\_0 - a + 1 > 0$, and $q: \forall t \in (0,1)$, the equation ${x^2 + \frac{y^2}{t^2 - (2a+2)t + a^2 + 2a + 1} = 1}$ always represents an ellipse with foci on the $y$-axis. If the disjunction $p \vee q$ is true and the conjunction $p \wedge q$ is false, find the range of values for the real number $a$.

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