
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 $Q$:
$P$: For all $x \in [-1, 2]$, $x^{2} - a \geq 0$;
$Q$: For all $x \in \mathbb{R}$, $2x^{2} + ax + 1 > 0$ is always true.
If $P \land Q$ is a false proposition and $P \lor Q$ is a true proposition, find the range of values for $a$.

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