
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
Suppose we have the proposition $p$: For all $x \in \mathbb{R}$, $x^2 + x > a$, and the proposition $q$: There exists $x \in \mathbb{R}$, such that $x^2 + 2ax + 2 - a = 0$.
(1) Write the negations of the two propositions $\neg p$ and $\neg q$;
(2) If the proposition $(\neg p) \vee q$ is false, determine the range of values for the real number $a$.

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