
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 two propositions $p$ and $q$: Proposition $p$ states that the equation $\frac{{{x}^{2}}}{2-a}-\frac{{{y}^{2}}}{a+1}=1$ represents a hyperbola, and proposition $q$ states that the equation ${x}^{2}-4x-a=0$ has real roots. If the negation of $p$ and $q$ is true, find the range of real number values for $a$.

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