
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
Let proposition p be: For all $m \in [-1, 1]$, the inequality $a^{2} - 5a - 3 \geq \sqrt{m^{2} + 8}$ always holds.
Let proposition q be: The domain of the function $f(x) = \log(x^{2} - 4x + a^{2})$ is $\mathbb{R}$.
If the proposition “p ∨ q” (p or q) is true and “p ∧ q” (p and q) is false, find the range of real numbers for a.

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