
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
Solve for the set of solutions to the quadratic inequality $-x^2 - 2x + 3 < 0$. Additionally, if the set of solutions to the quadratic inequality $-x^2 - 2x + a < 0$ is the entire set of real numbers $\mathbb{R}$, find the range of values of the real number $a$.

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